On the Apollo 14 mission to the moon,

Question

On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a golf club improvised from a tool. The acceleration free-fall on the moon is 1/6 of its value on earth. Suppose he hit the ball with a speed of 27 m/s at an angle 30 ∘ above the horizontal.

How long was the ball in flight?

How far did it travel?

How much farther would it travel on the moon than on earth?

Answer 1

Hi James!

Let's start by visualizing what's happening on a physical level. This is a special type of kinematic motion called projectile motion, during which there is only one force acting on the object... gravity!

The resulting motion will resemble a parabola (if this is an unfamiliar idea, I encourage you to look up such graphs!). In order to solve these kinds of problems, we use the important physics tool of componentizing the velocity vector (breaking it down into its vertical and horizontal components).

Now let's turn to the problem at hand. When Alan launches the ball, the vertical velocity component will be gradually reduced by the vertical gravity force (according to the formula vy = 27sin(30) - at, where vy is the vertical velocity and a is the acceleration which in this case is g/6). When vy is 0, the ball will be at the top of its parabola and will follow a symmetric arc back to Earth. We use this symmetry to say that

t = 27sin(30)/(g/6) * 2 (we multiply by 2 to account for both sides of the parabolic motion!)

b) Now we turn to the horizontal component of the velocity which does not change, because there is no horizontal force! We can say, then, that the total horizontal distance the ball travels is equal to

27cos(30) * t, where t is the time value we calculated above.

c) Let's think about what changes on Earth as opposed to the moon. The horizontal velocity will remain the same (there is still no horizontal force). The only thing that changes is the strength of the vertical gravity force and, as a result, the total amount of time the ball is in the air. Because the gravity force on the moon is 6x weaker than on the Earth, the ball will stay in the air for 6x longer, and, as a result, it will travel 6x as far on the moon.

I hope this helps!