A $69\mathrm{.}5-$kg athlete leaps straight up into the air from a trampoline with an initial speed of $7\mathrm{.}8$ 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?Score: $1$ out of $1$Comment:$($b$)$ Select the height at which the athlete's speed is $7\mathrm{.}8$ m$/$s as y $=0.$ What is her kinetic energy at this point? Correct: Your answer is correct. JWhat is the gravitational potential energy associated with the athlete? Correct: Your answer is correct. J$($c$)$ What is her kinetic energy at maximum height? Correct: Your answer is correct. JWhat is the gravitational potential energy associated with the athlete? Correct: Your answer is correct. J$($d$)$ Write a general equation for energy conservation in this case and solve for the maximum height. Substitute and obtain a numerical answer. Correct: Your answer is correct. 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.