# Homework Help: Projectile motion- acceleration due to gravity on the moon

1. Sep 26, 2008

### aurorabrv

1. The problem statement, all variables and given/known data
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 18 m/s at an angle 45 degrees above the horizontal.

a) How much farther did the ball travel on the moon than it would have on earth? (answer in m)

b) For how much more time was the ball in flight?

2. Relevant equations

3. The attempt at a solution

I don't really know where to start at all, any hints for what to do would be greatly appreciated!

a)
18cos45= 12.73
18sin45= 12.73

2. Sep 26, 2008

### Janus

Staff Emeritus
Do you know how to figure out how long it would be in flight if it was hit straight upward at a given speed?

3. Sep 26, 2008

### aurorabrv

Nope, I've never taken physics before, I'm pretty lost.

Would this be it?
y = y(i) + v(i)*sin(theta)*t + 1/2*g*t^2

Last edited: Sep 26, 2008
4. Sep 26, 2008

### Wecht

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 18 m/s at an angle 45 degrees above the horizontal.
a) How much farther did the ball travel on the moon than it would have on earth? (answer in m)
b) For how much more time was the ball in flight?

To start off, list what you know, it'll help you find a way to find what you're looking for. You know that
y-initial = 0m ax= 0 xf=?
x-initial = 0m ay=1/6[-9.81m/s(squared)] yf=0m (it lands back on the surface)
Vix=? t=? Vfx=?
Viy=? Vfy=?
Vi=18m/s
First, split the velocity into its x-component and y-component
Vix=cos45(Vi)
Viy=sin45(Vi)
now, you have everything you need to use yf=yi +Viyt + 1/2ayt(squared) to find time (on the moon)

after you've found the value of time, use the same equation for the x-component to find xf, which will be where the ball lands relative to the initial point. (on the moon)
xf = xi + Vixt +1/2axt(squared)

Now, on Earth, the initial velocities (both components), as well as x-initial, and y-initial and y-final will be the same as they were on the Moon. However, ay will now be
-9.8m/s(squared). So use that in the yf=yi +Viyt + 1/2ayt(squared) equation to find time (on Earth) and compare it to the time on the Moon. Then, using that time in that equation's x-component counterpart, find xf (on Earth) and compare that to the xf you calculated on the Moon.
Hope this helps, good luck!