A 48.1-kg athlete leaps straight up into the air from a trampoline with an initial speed of 9.6 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?
(b) Select the height at which the athlete's speed is 9.6 m/s as y = 0. What is her kinetic energy at this point? What is the gravitational potential energy associated with the athlete?
(c) What is her kinetic energy at maximum height? What is the gravitational potential energy associated with the athlete?
(d) Write a general equation for energy conservation in this case and solve for the maximum height. (Do this on paper. Your instructor may ask you to turn in this work.)
(e) Substitute and obtain a numerical answer.
(f) Write the general equation for energy conservation and solve for the velocity at half the maximum height.
(g) Substitute and obtain a numerical answer.