YA Physics!!?

Question

A high jumper, falling at -4m/s lands on a foam pit and comes to rest, compressing the pit .40m. If the pit is able to exert an avg force of 1200N on the high jumper in breaking the fall, what is the athletes mass???

lets see who the smartest and quickest one is out of this elite bunch...

This problem is trivial. The work the mat does on the athlete is 1200 N * (-.4 m). This work goes into slowing the athlete, reducing his kinetic energy.

Thus,

Fd = 1/2 m(v_f)^2 - 1/2m(v_i)^2
1200N * (-.4 m) = - 1/2 m (4 m/s)^2

Plug in and solve to give m = 60 kg.

ya I knew how to solve it!!

Answer 1

I'm smart enough to tell you to do your own homework kid.

You know the stopping distance, the initial velocity, and the final velocity (0 m/s). Using the equations of motion you should be able to find one that uses all those variables and will give you the acceleration as the only unknown. Solve for the acceleration.

Since
F = M * A
and you know the average force and have calculated the accleration, you can now calculate the mass on your own

EDIT: Karman, It's a homework problem. They're considering the foam pit to be compresable without any spring characteristics. sheesh.

Answer 2

Is this a high jumper in space? Question is interesting in that you have a body with constant velocity.... Think about that for a moment, and how to construct such a situation. Anyhow, you give this one difficulties in that the question states " ... comes to rest, compressing the pit .4m." This would mean a equilibrium state. Foam pit would have properties of a damped spring. The damping would result in one of three configurations:

1) Weakly damped: body compresses spring beyond equilibrium point and oscillates to a stop.

2) Heavily damped: initial velocity is reduced to a value that will not bring the body past the equilibrium point.

3) Equivalence: spring force and damping result in velocity decrease exactly to the equilibrium point.

The equilibrium point itself is calculated by Newtons law:

F = MA

where the force of the foam spring is equivalent to the mass of the body multiplied by the gravitational constant.

However, as you have given a constant velocity as a initial condition, this body is not in free fall. It has either reached its terminal velocity for the given conditions, or is not under gravitational acceleration (which would not make this a high jump...).

This may not be the answer you were looking for if this was a homework question, but, if you point out the fallacy of the question, you may incur accolades (or wrath) from your instructor. Of course the pedantic obvious answer to integrate Newton and plug in the values...

Answer 3

enjoy your OWN smartness.