A $70\mathrm{.}5-$kg athlete leaps straight up into the air from a trampoline with an initial speed of $9\mathrm{.}3$ m$/$s$.$ The goal of this problem is to find the maximum height she attains and her speed at half maximum height.

$($a$)$ What are the interacting objects and how do they interact?

This answer has not been graded yet.

$($b$)$ Select the height at which the athlete's speed is $9\mathrm{.}3$ m$/$s as

y $=0.$

What is her kinetic energy at this point?

J

What is the gravitational potential energy associated with the athlete?

J

$($c$)$ What is her kinetic energy at maximum height?

J

What is the gravitational potential energy associated with the athlete?

J

$($d$)$ Write a general equation for energy conservation in this case and solve for the maximum height. Substitute and obtain a numerical answer.

m

$($e$)$ Write the general equation for energy conservation and solve for the velocity at half the maximum height. Substitute and obtain a numerical answer.

m$/$s