As part of a fitness assessment, Bill must jump straight up to determine his vertical leap. If his mass is 70kg and his initial vertical velocity is 4m/s up:

Question

(a) What is Bill’s maximal kinetic energy?

(b) What is Bill’s minimal kinetic energy and when does it occur?

(c) What is Bill’s maximal potential energy?

(d) How high does Bill elevate his centre of mass at the peak of the jump?

Answer 1

a. KE = (1/2) m v² at maximum velocity you'll find the maximum KE because mass doesn't change.

(1/2) (70kg) (4 m/s)²

560J

b. At v = 0, KE = 0. v = 0 at the height of the jump.

c. It must be 560J because at the height of the jump v = 0 and the only place the energy could go is into potential energy. This can be verified by calculating the maximum height of the jump, y = (1/2)(-10 m/s²)t² + (4 m/s) t, and using your favorite method of calculating the maximum for the parabola. You get hmax = 0.8 m.

U = m g h = 70 kg * 10 m/s² * 0.8m = 560 J

d. Answered as part of c.