"Solving Free-Falling Pole Vaulter Problem

[Pogorz]

Homework Statement

A pole vaulter comes down after barely clearing the hurdle. the hurdle is at a height "H" above the top of the soft mat on the floor. The mat has a thickness of "h". when the athlete lands on the mat he slows down at a constant rate so that his speed is 0 just before he hits the ground (suppose the mat can be squeezed to a negligible thickness).

a) Find the speed of the athlete just before he hits the mat.
b) Find the acceleration of the athlete while he is in the mat.
c) Sketch the graphs for y-t, v-t, and a-t.

Homework Equations

v^2=vi^2+2ad

The Attempt at a Solution

I solved for Vf (sqrt19.62H) in terms of H, and for acceleration (sqrt4.905H/h^2)in terms of H and h. it says to 'sketch' a graph, so should i just sketch graphs resembling y=x^2, y=x, and y=9.8 for y-t, v-t, and a-t respectively?

 

[kuruman]

If by "x" you mean time, yes. The vertical position is quadratic in time, the position is linear and the acceleration is constant. However, note that you graph should come in two pieces. One when he is free fall and the acceleration is - g and one when he has hit the mat and the acceleration is ... ?