Question

Marissa jumps 1.0 m down onto a walkway. Her downward motion stops in 0.020 seconds, and her mass is 60 kg. Using a kinematics equation, such as , one can find her velocity just before she reaches the ground.

If she forgets to bend her knees, which force is transmitted to her leg bones when she lands?

12 N
3000 N
13,000 N
59,000 N

Answer 1

@JoannaBlackwelder
Since she jumps down then she's in free--fall, so wouldn't the length in time be irrelevant?
a=g and F=ma...
or am I overlooking something?

Answer 2

That is what I was thinking also.

Answer 3

@ybarrap
Can you help? I'm not getting any of the possible answers provided.

Answer 4

I'm thinking the solution would be something along these lines. The girls falls 1 m. It takes a certain amount of time for this, call it \(t_{fall}\). At this point she is going a certain velocity, call it \(v\). Her initial velocity was \(u=0\). To stop, she decelerates in .02 seconds from this final speed. This is added to the acceleration of gravity. The final force would be the sum of both these accelerations and her mass:

Using http://en.wikipedia.org/wiki/Equations_of_motion#SUVAT_equations
$$
s=u+\cfrac{1}{2}gt_{fall}^2\\
-1=0-\cfrac{1}{2}9.81t_{fall}^2\\
t_{fall}=\sqrt{\cfrac{2}{9.81}}\\
v=u+gt\\
v=0-9.81t_{fall}\\
$$
The deceleration occurs in .02 seconds,
$$
a_f=\cfrac{dv}{dt}\\
=\cfrac{-9.81\times t_fall}{.02}\\
F=mg+m\times a_f\\
=m(-9.81+a_f)
$$

Answer 5

On the other hand, since we already accounted for gravity in the equations in the 1st place we may not need to do it again in the end. Check both ways.

Answer 6

If you following this process, you will get an answer like 13,000 N.

Answer 7

This is about 22 times the force of gravity!

Answer 8

13,000 N is the correct answer. thank you so much for the help @ybarrap and everyone else.