A golf ball of mass 45.9 g is launched from a height of

Question

8.0 m above the level of the green at a speed of 20.0 m/s.
At the maximum height above the green, the ball is moving at 12 m/s. Assume there is no air resistance acting on the ball. Calculate the following for the golf ball:
(b) the maximum height of the ball above the green

Answer 1

To find the maximum height of the ball above the green, we can use the conservation of energy principle. At the maximum height, all of the initial kinetic energy of the ball will have been converted into potential energy.

Initial kinetic energy: KE_initial = 0.5 * m * v_initial^2
KE_initial = 0.5 * 0.0459 kg * (20 m/s)^2
KE_initial = 0.5 * 0.0459 kg * 400 m^2/s^2
KE_initial = 0.5 * 18.36 J
KE_initial = 9.18 J

At the maximum height, the ball has zero kinetic energy and only potential energy. The total mechanical energy of the ball is conserved, so:

Total energy at maximum height = KE_initial + PE_max
PE_max = Total energy at maximum height - Initial kinetic energy

PE_max = m * g * h
h = (PE_max)/(m*g)

PE_max = KE_initial
h = KE_initial/(m*g)
h = 9.18/(0.0459 kg * 9.8 m/s^2)
h = 20 m

Therefore, the maximum height of the ball above the green is 20 meters.