A basketball player throws a chall - 1 kg up with an initial speed of his hand at shoulder height = 2.15 m Le gravitational potential energy ber ground level the ball leves 50%. (a) Give the total mechanical energy of the ball E in terms of maximum height Am it reaches, the mass m, and the gravitational acceleration g. (b) What is the height, hm in meters?

Complete Question:

A basketball player tosses a basketball m=1kg straight up with an initial speed of v=7.5 m/s. He releases the ball at shoulder height h = 2.15m. Let gravitational potential energy be zero at ground level

a) Give the total mechanical energy of the ball E in terms of maximum height hn it reaches, the mass m, and the gravitational acceleration g.

b) What is the height, hn in meters?

Answer:

a) Energy = mghₙ

b) Height, hₙ = 5.02 m

Explanation:

a) Total energy in terms of maximum height

Let maximum height be hₙ

At maximum height, velocity, V=0

Total mechanical energy, E = mgh + 1/2 mV^2

Since V=0 at maximum height, the total energy in terms of maximum height becomes

Energy = mghₙ

b) Height, hₙ in meters

mghₙ = mgh + 1/2 mV^2

mghₙ = m (gh + 1/2 V^2)

Divide both sides by mg

hₙ = h + 0.5 (V^2) / g

h = 2.15m

g = 9.8 m/s^2

V = 7.5 m/s

hₙ = 2.15 + 0.5 (7.5^2) / 9.8

hₙ = 2.15 + 2.87

hₙ = 5.02 m