Given,
Frequency of the wave, f=4 Hz
The wavelength of the wave, λ=0.5 m
The speed of a wave is given by,
[tex]v=f\lambda[/tex]On substituting the known values in the above equation,
[tex]v=4\times0.5=2\text{ m/s}[/tex]Therefore the speed of the standing wave produced is 2 m/s
Explain how electron microscopy has increased understanding of subcellular structures.
[2]
Answer:
The development of the electron microscopes therefore helped scientists to learn about the sub-cellular structures involved in aerobic respiration called mitochondria . The scientists developed their explanations about how the structure of the mitochondria allowed it to efficiently carry out aerobic respiration.
Two trains leave the same station at the same time, one traveling west at a constant speed of 60 miles per hour, the other traveling south at a constant speed of 80 miles per hour. After how long are the two trains exactly 300 miles apart?
If one train travels at constant speed 60 miles/h and other train at 80 miles/h south and west respectively then after 3 hours the two trains are exactly 300 miles apart.
What is speed?Speed is a scalar quantity that indicates how quickly an object is moving, regardless of its direction.
The formulas below can be used to determine an object's speed:
S = d/t
where
d is the distance an object travels and
where
The metre per second (m/s) is the unit of speed in the SI system.
As the train are traveling south and west the angle of direction between them is 90° hence we can use Pythagoras theorem to find displacement
c = √(a² + b²)
displacement of 1 hour = √(60 ² + 80²)
= √10000
= 100 miles
time taken 100 miles is = 1 hour
Then time taken for displacement of 300 miles = 3 × 1 hour
= 3 hours
Thus, After 3 hours the two trains are exactly 300 miles apart.
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If 1000 J of work is used to raise a 20-kilogram crate to a high shelf in a warehouse, how high was the crate
raised?
The height at which the 20 kilogram crate is raised to, in the warehouse is approximately 5.1 meters.
What is the height of the crate?Work done is simply defined as the energy transfer that takes place when an object is either pushed or pulled over a certain distance by an external force.
It is expressed as;
Work done = force × distance
Given the data in the question;
Work done = 1000J = 1000kgm²/s²Mass of the crate m = 20kgHeight ( distance ) h = ?Note that;
Force = mass × acceleration
But since the crate is raised and under gravity.
Force = mass × acceleration due to gravity
F = mg
Hence;
Work done = mg × h
1000kgm²/s² = 20kg × 9.8m/s² × h
1000kgm²/s² = 196kgm/s² × h
h = 1000kgm²/s² ÷ 196kgm/s²
h = 5.1m
Therefore, the height of the crate is 5.1 meters.
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Which object could be used as a earth model a hard boiled egg or glass marble or ping-pong ball or watermelon 
As the earth surface is protecting the molten material present at the center of the earth that has different propeerties than the material on the earth surface.
The hard boiled egg also consist of yolk at the center consisting of most the nurtients and different properties from its surface. The outer shell of the egg protect the inner side of the egg.
Thus, the hard boiled egg can represent the earth model.
Skydivers accelerate downward when they first jump out of an airplane. Eventually they reach a terminal velocity, however, and their speed remains constant because two forces become equal in magnitude but opposite in direction. What are these two forces?
Take into account that the gravitational force implies an acceleration on the skydivers when they go downward. While they go down the drag force, due to the air, decelerates the motion of the skydiver. The drag force increases in a constant way (becasue the drag force depends on the speed of the skydiver, and the speed, due to the acceleration produced by the gravity, increases), until it equals the gravitational force and the speed of the skydiver becomes constant.
Hence, the two forces are the gravitational force and the drag force
A projectile is launched at an angle of 30° above the horizontal with an initial velocity (vo) of 42.2 m/s. After some time passes, the projectile reaches the peak of its trajectory.Its horizontal velocity (vx) at the peak of its trajectory is ____ m/s.
First, for us to start, let us draw the problem:
When we analyse this problem, we can see that the only velocity that changes overtime is the vertical velocity (due to gravity), so the horizontal speed is the same throughout the whole movement. This gives us the following:
[tex]v_x=42.2*cos(30°)=36.546\frac{m}{s}[/tex]Then, the horizontal speed at the peak of the trajectory (and also during the whole movement) is v=36.546m/s
A car accelerates uniformly, passing a first checkpoint with velocity 20 m s-1, andpassing a second checkpoint with velocity 32 m s-1, after 4 seconds.a)Sketch a velocity-time graph to show this information.b)Use the velocity-time graph to find each of the following.C)The acceleration of the car during the 4 seconds.The total distance travelled by the car during the 4 seconds.
Part a: velocity-time graph
Where t is time in seconds after reaching the first checkpoint.
Part b:
Acceleration = change in velocity/time
a = (v2-v1)/t
v2: final velocity, v1: initial velocity, t: time
Let's keep track of all the variables we know:
v2 = 32 m/s, v1 = 20 m/s, t = 4 s
Now let's plug all the known variables in:
a = (32-20)/4 = 12/4
a = 3 m/s^2
d = (v1)*t + (a*t^2)/2
Let's keep track of all the variables we know:
v1 = 20 m/s, t = 4 s, a = 3 m/s^2
Now let's plug all the known variables in:
d = 20*4 + (3*4^2)/2 = 80 + 48/2 = 80 + 24
d = 104 m
/s
A baseball player is dashing toward home plate with a speed of 5.6 m/s when she decides to hit the dirt. She slides for 1.5 s , just reaching the plate as she stops (safe, of course). Calculate the acceleration.
ANSWER:
-3.73 m/s^2
STEP-BY-STEP EXPLANATION:
Acceleration is the rate of change of velocity and we can calculate it as follows:
[tex]a=\frac{v_2-v_1}{\Delta t}[/tex]Replacing:
[tex]\begin{gathered} a=\frac{0-5.6}{1.5} \\ a=-3.73m/s^2 \end{gathered}[/tex]The baseball's player's deceleration is 3.73 m/s^2
A force of magnitude Fx acting in the x-direction on a 2.35-kg particle varies in time as shown in the figure below. (Indicate the direction with the sign of your answer.)
The impulse is mathematically given as
v_f=3.61m/s
This is further explained below.
What is impulse?Generally, In classical mechanics, the integral of a force F over the time period t during which it operates is referred to as the impulse of the system.
It should come as no surprise that impulse is likewise a vector quantity given that force is one.
When an impulse is applied to an item, a corresponding vector change in the object's linear momentum occurs, also in the direction that the impulse causes.
In conclusion, Impulse = Area Under Curve
=2*4+1*4
[tex]m\left(v_f-v_i\right)=12 \\\\v_f=\frac{12}{2.35}=5.11 \mathrm{~m} / \mathrm{s}\\\\m\left(v_f-(-1.5)\right)=12 \\v_f=5.11-1.5 \\\\ =3.61 \mathrm{~m} / \mathrm{s} \\v_f=3.61 \mathrm{~m} / \mathrm{s}\end{gathered}$$[/tex]
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CQ
A force of magnitude Fx acting in the x-direction on a 2.35-kg particle varies in time as shown in the figure below.
(a) Find the impulse of the force.
____________kg
What is discharged body
A body is considered to be discharged when it loses charge to the ground or another body.
The human body is an excellent conductor. Therefore, that will fall to the earth as the Charge passes through our bodies. Discharge of the body is the process by which the excess energy leaves the body and flows through it before falling to the ground. The term "earthing" refers to this idea.
Allowing the electricity to discharge from your body into the ground is the quickest approach to eliminating static electricity from the body. Touch any conductive object that is not isolated from the ground to enable this, such as a metal light pole or the screw on a light switch panel.
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Which is true about a step-down transformer?Voltage out is larger than the voltage in.Voltage out is smaller than voltage in.It is when a robot turns into a car.Voltage out is the same as the voltage in.
Answer:
Explanation:
A step down transformer decreases the incoming voltage. It converts high voltage and and low current from the primary side to low voltage and high current. Thus, the correct option is
Voltage out is smaller than voltage in.
A 100-g ball is launched from the ball launcher in a pinball machine (pictured below). The force constant of the spring is 110 N/m. The spring is initially compressed 4.0 cm and the coefficient of kinetic friction is 0.2. Hint: watch your units!
a) How fast is the ball going when it passes the equilibrium point of the spring?
b) How far will the ball go up the ramp? Specify clearly what value you are giving me!
The ball is going when it passes the equilibrium point of the spring with a speed of 1.26 m/s and the ball go up the ramp till a height of 8.1cm.
The mass of the ball is 0.1 Kg. The force constant is 110N/m. The compression in spring is 4 cm which is equal to 0.04 meters. The coefficient of kinetic friction is 0.2.
a) Applying work energy theorem, according to which the total work done on a body by all the forces us equal to the net change in kinetic energy of the body.
Total work done = change in kinetic energy
Work done by friction + work done by spring = ∆KE
umgx + 1/2Kx² = 1/2mv²
Where,
u is the coefficient of kinetic friction,
m is the mass of the the ball,
g is acceleration due to gravity,
K is spring constant,
v is the velocity of the ball,
x is the compression in the spring.
Putting all the values,
-0.2(0.1)(9.8)(0.04) + (0.5)(110)(0.04)(0.04)= (0.5)(0.1)v².
-0.00784 + 0.088 = 0.05v²
v²=1.6
v = 1.26 m/s.
b) Applying energy conservation,
Initial total energy = final total energy
Mgh = 1/2Mv²
(0.1)(9.8)h = (0.5)(0.1)(1.6)
h = 0.081m
h = 8.1 cm.
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A track and field athlete is competing in the hammer throw event. The athlete is 181cm tall, with an arm length of 90 cm and is using a standard ball and chain for the event which is 121cm long. As the athlete begins to spin , their body becomes the center of the motion, with both arms holding on to the ball and chain handleIf the initial linear ve locity of the ball and chain is 29m/s upon its release, how fast (total angular velocity rads) was the athlete spinning it.
The angular velocity is obtained from the calculation as 13.7 rad/s.
What is the angular velocity?Let us recall that the term circular motion is applied to the kind of motion that is carried out by an object that is moving along a circular path. Given the fact that we have an object that is spinning around in a circular path, we can say that a circular motion is actually taking place in the system that involves the athlete, the ball and the rope.
We are told that the athlete is 181cm tall, with an arm length of 90 cm and is using a standard ball and chain for the event which is 121cm long. As the athlete begins to spin , their body becomes the center of the motion, with both arms holding on to the ball and chain handle then the initial linear velocity of the ball and chain is 29m/s upon its release.
We can now see that the radius of the path is 90 cm + 121 cm = 211cm or 2.11 m
Using;
V = rω
ω = V/r
ω = 29m/s/2.11 m
ω = 13.7 rad/s
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A train accelerates at a constant rate of 1 m/s2. It passes through a 24.5 m wide level crossing in a time of 2 s. After the train leaves the crossing, how much time is required until its speed reaches 31 m/s?.
A train accelerates at a constant rate of 1 m/s², then the velocity of the train after time t₁ will be equal to 15.25 m/s.
What is Velocity?Velocity is really the direction speed of an item in motion as a measure of the rate at which its location is changing as seen through a particular point of view and as determined by a specific unit of time. A key idea in kinematics, the area of classical physics that studies how bodies move, is velocity.
Acceleration, a = 1 m/s²
Distance, d = 24.5 m
Time, t = 2 s
Velocity, v₂ = 31 m/s
By the equation of motion,
v = u + at
v = v₁
t = t₁
v = v₁ - 4.2 (1)
24.5 = u(2) + 1/2(1)(2²)
u = 11.25 m/s
v₁ = u + 4
v₁ = 11.25 + 4
v₁ = 15.25 m/s.
Therefore, the velocity of the train after time t₁ is 15.25 m/s.
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Fg = Fc. How can the gravitational force be equal the the centripetal force when both forces are pointing inwards?
ANSWER and EXPLANATION
A centripetal force is a force acting on an object that keeps it moving in a circular path.
Gravitational force is an attractive force acting between two objects.
Gravitational force can only be equal to centripetal force when the gravitational force (attractive force) is the only force keeping that object moving in a circular path. In this case, we can say that the gravitational force is the centripetal force keeping the object in orbit.
Mathematically, we can write that:
[tex]\begin{gathered} F_g=F_c \\ \\ \frac{Gm_1m_2}{r^2}=\frac{m_1v^2}{r} \end{gathered}[/tex]where G = gravitational constant
m1, m2 = masses of the two objects
r = distance between the objects
v = velocity of the object in consideration
You are driving your 1800 kg car at 21 m/s over a circular hill that has a radius of 150 m. A deer running across the road causes you to hit the brakes hard while right at the summit of the hill, and you start to skid. The coefficient of kinetic friction between your tires and the road is 0.75.
What is the magnitude of your horizontal acceleration as you begin to slow?
The magnitude of your horizontal acceleration as you begin to slow is 7.35m/s².
Applying work-energy theorem,
Total work done on the body by all the forces = change in kinetic energy.
So, here,
Work done by friction = ∆KE
-uMgd = 1/2M(v²-u²)
u is the coefficient of friction,
M is the mass of the car,
g is the acceleration due to gravity,
v is the final velocity of car,
u is the final velocity of car,
d is the horizontal distance moved by car.
(-0.75)(1800)(9.8)d = -1/2(1800)(21)²
d= 30 meters.
Applying Equation of motion,
V²-U²=2ad
Where a is the horizontal acceleration,
-(21×21) = 2(30)a
a = 7.35m/s².
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This diagram shows an object with a mass of 3kg being pushed along africtionless surface. The object accelerates at 3m/s/s. What force was applied tothe object? *
We are asked to determine the force exerted on the object. To do that we will use Newton's second law:
[tex]F=ma[/tex]Where:
[tex]\begin{gathered} F=\text{ force} \\ m=\text{ mass} \\ a=\text{ acceleration} \end{gathered}[/tex]Now, we substitute the values:
[tex]F=(3kg)(3\frac{m}{s^2})[/tex]Solving the operations:
[tex]F=9N[/tex]Therefore, the force is 9N.
A bar magnet is cut into two pieces from the middle as shown in the figure. Mark the poles on these magnets if it is further broken into smaller pieces?
If the longer magnets is cut into bits, the bits become smaller magnets having north south poles.
What is a magnet?The magnet is a substance that is composed of the North and the south poles and is able to attract the objects that we call magnetizable. These magnetizable materials do have their magnetic fields aligned appropriately there.
We know that if we cut a magnet then what we are going to generate is a number of smaller magnets that can also be able to attract magnetizable materials each of the magnets would also have a north - south pole.
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What would be the pressure of 1.0 g of O2 contained in a 4.00 L container at 293 K?
Use the Ideal Gas Law to find the pressure of the gas under the given conditions:
[tex]PV=nRT[/tex]Where P represents pressure, V represents volume, n represents the amount of substance of the sample, R is the universal gas constant and T represents the temperature.
The volume and the temperature of the sample are given. On the other hand, we can calculate the amount of substance from the given mass of the sample. The molar mass M of a substance is the ratio between the mass of a sample and the amount of substance, and is characteristic of each substance:
[tex]M=\frac{m}{n}[/tex]A molecule of O₂ is made of two oxygen atoms. The atomic mass of oxygen is approximately 16u, then, the atomic mass of the molecule of O₂ is 32u, which means that its molar mass is 32 grams per mole:
[tex]M_{O_2}=32\frac{g}{mol}[/tex]Isolate n from the equation and replace m=1g and M=32g/mol to find the amount of substance of the sample:
[tex]n=\frac{m}{M}=\frac{1g}{32\frac{g}{mol}}=0.03125mol[/tex]Now that we have calculated the value of n, the only unknown for the Ideal Gas Law is the pressure of the gas. Write the universal gas constant using units of liters for the volume:
[tex]R=8.314\frac{J}{mol\cdot K}=8.314\frac{L\cdot kPa}{mol\cdot K}[/tex]Isolate P from the ideal gas law and replace V=4.00L, n=0.03125mol, T=293K and the value of R to find the pressure of the gas:
[tex]\begin{gathered} PV=nRT \\ \\ \Rightarrow P=\frac{nRT}{V} \\ \\ =\frac{(0.03125mol)(8.314\frac{L\cdot kPa}{mol\cdot K})(293K)}{4.00L} \\ \\ =19.031...kPa \\ \\ \therefore P\approx19kPa \end{gathered}[/tex]Therefore, the pressure of the container will be approximately 19kPa.
what is the fraction form 4.75
Given, the number which should be converted to fracton is 4.75
We can convert it to a fraction in the following way
[tex]4.75=\frac{475}{100}[/tex]We can simplify the above fraction by dividing numerator and denominator by 5
That is
[tex]\frac{475}{100}=\frac{95}{20}[/tex]We can further simplify it by again dividing numerator and denominator by 5.
Thus,
[tex]4.75=\frac{19}{4}[/tex]Thus the fraction form of 4.75 is 19/4
A technician examines different electrical devices to determine the one that is the most energy efficient. While conducting a test, he notes that one of these devices consumes 550 000 J of energy and loses 315 000 J at the same time. What is the energy efficiency of this device?
The output of this device is equal to 550 000-315 000 = 235 000, or 42.7%, of its energy efficiency.
What does "machine efficiency" mean?Efficiency is the percentage of input work that is actually completed by the machine (output work). The fact that some of the input work is used to reduce friction is the main cause of the output work always being less than the input labor. Efficiency is never 100% and is therefore always less than 100%..
How effective is a basic machine?Due to internal friction, simple machines are always less efficient than 1.0. conserving energy When friction is ignored, the work performed on a simple machine is equivalent to the work performed by the machine to complete a task.
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which statement describes a characteristic of an experimental design that will improve the quality of the results?
To establish cause and effect linkages, the experimental approach manipulates variables. The use of controlled methodologies and the assignment of participants at random to control and experimental groups are the main characteristics.
The caliber of the outcomes?A. A bigger sample will provide you better precision because more subjects will be under observation.
B: The complexity of the technique increases the likelihood that the scientist will make a mistake and taint the data. As a result, the quality is not improved.
C: When we change just one variable, we run the risk of adding some inaccuracy into the data.
For instance, if the amount is the voltage for an experiment, there is a minor source of inaccuracy because we do not exactly know the precise voltage that originates from the source. An experiment with multiple independent variables won't increase the quality of the results since as we start adding more independent variables, we are also adding more of these sources of error.
D. A study with a large number of dependent variables.
Similar to how changing the variable A changes the variables B, C, and K.
You will now notice changes in the variables C, B, and k as you experiment with the variable A.
However, there is now a query (a lot actually)
if the alteration in C actually brought about the alteration in K?
The next step is to create an experiment to investigate what happens when the value of C is changed for a fixed value of A.
This might be really challenging, thus the simpler the experiment is and the easier it is to gather useful data, the better.
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What happens when sunlight strikes a photovoltaic cell? A. small tubes of water are heated, producing a flow of energyB. carbon dioxide is released as a waste productC. electrons are released, causing a flow of electrical currentD. atoms are split, resulting in a release of energy
When sunlight strikes on a photovoltaic cell, the electrons are released, causing a flow of electrical current.
Hence, the correct asnwer is option (C)
Two 3.09 cm by 3.09 cm plates that form a parallel-plate capacitor are charged to +/- 0.617 nC. What is the electric field strength inside the capacitor if the spacing between the plates is 1.784 mm?
Given:
The charge on the capacitor is Q = 0.617 nC
The distance between plates is d =1.784 mm
The area is
[tex]\begin{gathered} A=\text{ 3.09}\times3.09 \\ =9.5481\text{ cm}^2 \end{gathered}[/tex]To find the electric field strength.
Explanation:
The electric field strength can be calculated by the formula
[tex]E=\frac{Q}{\epsilon_oA}[/tex]The constant is
[tex]\epsilon_o=8.85\times10^{-12}\text{ C}^2\text{ / N m}^2[/tex]On substituting the values, the electric field strength will be
[tex]undefined[/tex]
Question 2 of 25If the law of conservation of energy applies to a situation, then:A. the system is an open one.B. the output work being done is greater than the work being put into the system.C. the total (PE + KE) before an event is equal to the total (PE+KE) after the event.D. matter is entering and leaving the system.
ANSWER
C. The total (PE + KE) before an event is equal to the total (PE + KE) after the event.
EXPLANATION
We want to identify the correct option.
The law of conservation of energy is a law that applies only to closed systems and it states that:
In other words, energy cannot be created nor destroyed.
This implies that the total energy (sum of potential and kinetic energy) before an event occurs must be equal to the total energy after the event has occurred.
Therefore, the correct option is option C.
7/21/22, 7:37 AMProblem Set ThreeNotes: Use 9.8 m/s 2 for the acceleration due to gravity. Formust be expressed in m/sLaw calculations, mass must be expressed in kg and velocity.A man with a mass of 110kg slides down a vertical pole with an acceleration of 9 m/s2. What is the frictional force acting on the man?
Given:
The mass of the man is m = 110 kg
The man slides down with acceleration,
[tex]a=9\text{ m/s}^2[/tex]The acceleration due to gravity is
[tex]g=\text{ 9.8 m/s}^2[/tex]Required: The frictional force acting on the man.
Explanation:
The equation of motion to calculate frictional force is given as
[tex]\begin{gathered} mg-f=ma \\ f=mg-ma \\ =m(g-a) \end{gathered}[/tex]On substituting the values, the frictional force will be
[tex]\begin{gathered} f=110(9.8-9) \\ =\text{ 88 N} \end{gathered}[/tex]Final Answer: The frictional force is 88 N
A dog was running 10.8m/s for 61s. How far did it run in that time?
To solve using these three variables, we can use this equation:
distance = speed × timeSolving the QuestionWe're given:
Speed: 10.8 m/sTime: 61 sDistance: ?⇒ Plug the given values into the equation:
distance = speed × time
distance = 10.8 m/s × 61 s
distance = 658.8 m
AnswerThe dog ran 658.8 m in that time.
A psychology professor testified as an expert witness in court on behalf of a man who was hit by a train. In his testimony, the professor noted that it is reasonable to believe that someone who lives next to train tracks might not even notice an approaching train. Which term does this situation exemplif
Habituation is a term does this situation exemplify.
In this case, the professor is talking about a situation where a person has become used to a particular stimulus. as a result, the rate at which the stimulus would be registering to the person would be much lesser as compared to someone who is fairly new in being exposed to the stimulus.
This process is called habituation. Sensitization is the situation where a person becomes extremely sensitive to even lower intensity of the stimulus.
Habituation is a form of non-associative studying in which an innate reaction to a stimulus decreases after repeated or prolonged presentations of that stimulus. Responses that habituate encompass those who involve the intact organism or those that contain simplest additives of the organism.
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On July 19, 1969, the lunar orbit of Apollo 11 was adjusted to an average height of 172 kilometers above the Moon's surface. The radius of the Moon is 1840 kilometers, and the mass of the Moon is 7.3 x 1022 kilograms. At what speed did the spacecraft orbit the Moon? Include units in your answer. Answer must be in 3 significant digits.
In order to calculate the speed of the spacecraft, use the following formula;
[tex]v=\sqrt[]{\frac{GM}{r}}[/tex]where,
M: mass of the moon = 7.3*10^22 kg
G: Cavendish constant = 6.67*10^-11 Nm^2/kg^2
r: distance in between the spacecraft and the center of the Moon =
172 km + 1840 km = 2012 km
Replace the previous values of the parameters into the formula for v and simplify:
[tex]v=\sqrt[]{\frac{(6.67\cdot10^{-11}N\frac{m^2}{\operatorname{kg}^2})(7.3\cdot10^{22}kg)}{2012\operatorname{km}}}\approx4.91\cdot10^4\frac{m}{s}[/tex]Hence, the speed of the spacecraft is approximately 4.91*10^4 m/s
The SPH3U class designs a cannon able to shoot a human being out of it. . If the human is launched at a velocity of 40 m/s, 37° from the ground, how far from the cannon should you place a mattress to catch the human if the muzzle of the cannon is 0.75 m from the ground?
Given:
Velocity = 40 m/s
Angle = 37°
Let's find the distance from the cnnon where you should place a matress to catch the human if the muzzle is 0.75 meters from the ground.
Let's first draw the projectile motion diagram:
To find the distance, first apply the formula to solve for the time taken for the human to reach the matress.
[tex]y=y_o+v_{oy}t-\frac{1}{2}gt^2[/tex]Where:
Height from the ground to the muzzle = yo = 0.75
y = 0
Velocity = vo = 40 m/s
initial vertical velocity = voy = vo sinθ = 40 sin37
We have:
[tex]v_{oy}=v_o\sin \theta=40\sin 37=24.07\text{ m/s}[/tex]g is the acceleration due to gravity = 9.8 m/s²
Now, let's solve for the time t:
[tex]\begin{gathered} y=y_o+v_{oy}t-\frac{1}{2}gt^2 \\ \\ 0=0.75+24.07t-\frac{1}{2}\times9.8\times t^2 \\ \\ t=4.94\text{ seconds} \end{gathered}[/tex]To sove for the horizontal distance, x, apply the formula:
[tex]\begin{gathered} x=v_{ox}t \\ \\ \text{Where:} \\ v_{ox}=v_o\cos \theta=40\cos 37=31.94\text{ m/s} \end{gathered}[/tex]Hence, we have:
[tex]\begin{gathered} x=31.94\times4.94 \\ \\ x=157.8\text{ m} \end{gathered}[/tex]Therefore, the matress should be placed at 157.8 meters from the cannon in order to catch the human.
ANSWER:
157.8 meters