Question

On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a 6 iron. The acceleration due to gravity on the moon is 1/6 of its value on earth. Suppose he hits the ball with a speed of 11m/s at an angle 15degree above the horizontal. a) How much farther did the ball travel on the moon than it would have on earth? b)For how much more time was the ball in flight?

Answer 1

Horizontal velocity = 11cos15 = 10.625 m/s

Vertical velocity = 11sin 15 = 2.847 m/s

Acceleration on earth = 9.8 m/s²

Acceleration on moon = -9.8/6 = 1.63 m/s²

b) Let time of flight on moon = 2t

So time for max height = t where v =0

In vertical direction

v = u + at

0 = 2.847 - 1.63t

t = 1.74 s

Let time of flight on earth = 2T

So time for max height = T where v =0

In vertical direction

v = u + at

0 = 2.847 - 9.81T

T = 0.29 s

More time required on moon = 2(1.74 - 0.29) = 2.90 s

a) Horizontal displacement on moon = 10.625 X 1.74 X 2 =36.98m

Horizontal displacement on earth = 10.625 X 0.29 X 2 =6.16 m

Extra distance travelled on moon = 36.98 - 6.16 = 30.82 m