How Do You Calculate Forces and Velocities in Physics Problems?

[chops369]

Homework Statement
Ok, I have a couple problems that I'm having trouble with. Bear with me, my physics teacher can be a little creative...lol.

1. I am an expert swan diver. If I am jumping off a 3m diving board, what is the velocity with which I strike the water? If the water brings me to rest in 0.3 seconds, what is the force the water applies to me?

2. Driving along in your 850 N Mini Cooper you pass by a hemp clothing yard sale and slam on your brakes. If you were traveling 20 m/s and your brakes apply a force of 8000 N in the opposite direction, how long does it take you to stop? How far do you skid?

3. Super Mario, who weighs 5 kg, is standing on a platform, which weighs 25 kg. Seeing Bowser in the distance he jumps off the platform with a speed of 3 m/s to the right. What is the final velocity of the platform?


Relevant equations
Vi = √2ghi
F∆t = -mVi/∆t
F∆t = mVf - mVi
m₁V₁,_i + m₂V₂,_i = m₁V₁,_f + m₂V₂,_f

I'm not sure if there are any others that I need, but I have a feeling that I'm missing something.

The attempt at a solution
For the first problem, I used Vi = √2ghi and found the man to be going 7.7 m/s. Then I tried to use the equation F∆t = -mVi/∆t, but I don't have the mass. Is there another equation to use or did my teacher just forget to include mass? (he does that a lot)

For the second one I think it has something to do with the impulse momentum theorem, but how would I find the skid distance with that?

For the third one, I'm pretty sure I need to use m₁V₁,_i + m₂V₂,_i = m₁V₁,_f + m₂V₂,_f. But I don't really know where to start.


EDIT: I just tried to solve number 3 and I got -0.6 m/s. Is this correct? I'm still not too sure about the other problems though.

 

[MalachiK]

All three of these questions can be solved by application of a relevant conservation law (energy or momentum). What you could do in each case is select a conserved quantity and then think about what is happening as the events in the question proceed.

You've used energy conservation to find the velocity of the diver just before they hit the water in question one. Try thinking about the physics behind that calculation and ponder what is going to happen next to the motion of the diver and their kinetic energy.

Likewise, in question two there is kinetic energy at the start and then later on...? Also, since you know the resultant force on the car and its mass you should be able to calculate the acceleration.

You may find it helpful to look up how to calculate the work done by a force (and what this term means!) for these first two problems.

You have the correct answer to question 3.

 

[nlightner]

I would say that you are on the right track with your solutions. Let's break down each problem and see if we can come up with a solution together.

1. In order to find the velocity with which you strike the water, we can use the equation Vf = Vi + at, where Vf is the final velocity, Vi is the initial velocity (which we found to be 7.7 m/s), a is the acceleration (which we know is -9.8 m/s^2 since the man is falling), and t is the time (which we know is 0.3 seconds). Plugging in these values, we get Vf = 7.7 + (-9.8)(0.3) = 4.9 m/s. This is the velocity at which the man hits the water.

To find the force the water applies to the man, we can use the equation F∆t = m(Vf - Vi), where F is the force, ∆t is the time, m is the mass (which we don't have, but we can assume it to be the mass of an average person, around 70 kg), Vf is the final velocity (which we just found), and Vi is the initial velocity (which we know is 7.7 m/s). Plugging in these values, we get F(0.3) = (70)(4.9 - 7.7), which gives us F = 1367.14 N. This is the force that the water applies to the man.

2. For this problem, we can use the equation F∆t = m(Vf - Vi) again, but this time we are looking for the time it takes to stop. We can rearrange the equation to solve for ∆t, which gives us ∆t = m(Vf - Vi)/F. Plugging in the values, we get ∆t = (850)(0 - 20)/8000 = -2.125 seconds. This is the time it takes for the car to come to a complete stop.

To find the skid distance, we can use the equation d = Vi∆t + 1/2at^2, where d is the distance, Vi is the initial velocity (which is 20 m/s), a is the acceleration (which is -8000 N/850 kg = -9.