Calculate Energy Loss from Parachutist Jump

[petern]

A parachutist with a mass of 50.0 kg jumps out of an airplane with an altitude of 1.00 x 10^3 m. After the parachute deploys, the parachutist lands with a velocity of 5.00 m/s. Find the energy that was lost to air resistance during th jump.

I tried using this: W = Kf – Ki → W = ½ mv^2 (f) – ½ mv^2 (i)
but I don't know what the initial velocity was because I don't know when the parachute deploys. How do you solve this problem?

 

[hage567]

The key is that you know the height he jumped from. What does that tell you about the energy he starts off with? You don't need to know when the parachute deploys. Since you know the velocity of the jumper when he reaches the ground, you know how much energy he has left when he reaches the ground.

 

[petern]

The key is that you know the height he jumped from. What does that tell you about the energy he starts off with? You don't need to know when the parachute deploys. Since you know the velocity of the jumper when he reaches the ground, you know how much energy he has left when he reaches the ground.

So I use V^2 = V_o^2 + 2ax and solve for V. Then I find the kinetic energy using this: W = Kf – Ki → W = ½ mv^2 (f) – ½ mv^2 (i). Is that right?

 

[hage567]

You don't need to worry about the initial velocity. What's gravitational potential energy? If you know that, you know how much energy he has to start off with.

 

[petern]

Here's another problem with the same concept but I can't seem to get it to work:

A horizontal force of 2.00 x 10^2 N is applied to a 55 kg cart across a 10 m level surface accelerating it 2 m/s^2. Find the force of friction that slows the motion slows the motion of the cart.

Is there enough information on friction? The method I used for the first problem doesn't work.

 

[Harmony]

Initially, the parachutist has gravitational potential energy and zero kinetic energy (since u=0). As the parachutist drops, he experiences a drop in gravitational potential energy, and the loss in energy is converted into the kinetic energy.

 

[petern]

Since there's no gravitational potential energy in the second problem, I would have to use velocity but there's not enough information on friction to find out what the final velocity is.

 

[Harmony]

You can either:
1) Apply Newton's Second Law. What is the resultant force? From there you can get your friction.

or

2) Apply Principle of Conservation of Energy. Resultant force x distance traveled = Change in Kinetic Energy

You are given the acceleration, so it doesn't matter if you don't know the magnitude of friction.