For how much more time was the ball in flight?
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 30.0 m/s at an angle 60.0 degrees above the horizontal.
How much farther did the ball travel on the moon than it would have on earth?
For how much more time was the ball in flight?
25. November 2006 at 1:46 pm :
on x axis we have no acceleration
then we hace a displacement equation vs t
x=30 cos 60 t ……. equation 1
on y axis we have an acceleation downward equal to g/6 where g=9,8 m/sec^2` the displacement equation is
y=30sin 60 t- 1/2 (g/6) t^2 ……. equation 2
from equation 1
t= x/30cos 60
replace t in equation 2 and remembering that sin/cos=tan
then
y =x tan 60 -1/2(g/6) x^2/(30cos60)^2 ….. equation 3
eq 3 gives the height of the ball in fonction of x. This is a quadratic equation.
using eq 3 , assume that when the ball hits the moon surface y=0
isolate x in this equation with y=0 and you have where the ball hit the moon
The time of flight is found with the value of x found and the eq 1
t= x/30 cos 60
Compare to the earth, it is easy to see that on the moon, the ball will go x 6 times farther
now take a piece of paper and and a pen and do your homeword
good luck
P.A.