00:01
So on the apollo 14 mission onto the moon, and the astronaut hit a golf ball with a six iron, and the free fall acceleration on the moon, so gm is equal to one sixth of its value on earth.
00:20
Right.
00:21
And he hits the ball with an initial speed of 26 meters per second at an angle 60 degrees above the horizontal.
00:35
And this implies that he's hitting it in this direction.
00:42
And we're going to have components.
00:46
We're going to have vy here, vx here, and this is our angle theta of 60 degrees.
00:54
A little more apparent.
00:58
So we know that thanks to sine and cosine, that sine of theta is equal to opposite over adjacent, over hypotenuse and cosine is equal to adjacent over hypotenuse.
01:19
And so we know that this is the opposite.
01:22
This is the hypotenuse and this is the adjacent.
01:25
And so we know that initial velocity in the y direction is going to be equal to v times sine theta.
01:36
And initial velocity in the x direction is going to be equal to v.
01:42
Cosine theta, which we'll use in a little bit for our kin -a -max equations.
01:49
For part a, or sorry, for part one, we would like to know how much farther did the ball travel on the moon than it would have on earth? and so we can use this equation, this kin -a -max equation, where we have v -final equals v -initial plus a times t, and we'll be looking at the y direction first.
02:20
And so earth, we'll do earth first.
02:29
We know that the final, the magnitude of the final is going to equal the magnitude of the initial because it's traveling in an arc, right? and so whatever v initial is when it starts is going to equal the magnitude of the final, but the final will have the opposite direction.
02:52
So this implies that v final is going to be equal to negative v .0.
03:00
So what we have here then is negative v0 equals v0 plus g times t.
03:11
And we'll label this t, te for t earth.
03:19
And so what we're going to get is negative 2v0 is equal to g times t.
03:27
T and we can divide it by g.
03:31
We get that time that the ball has been in the air on earth is going to be equal to negative 2 times v0 times g.
03:43
And now let's look at this equation for the moon.
03:47
We know that the initial and final velocity in the moon aren't going to change.
03:53
They're going to be the same thing, but what is going to change is g and t.
03:57
And so what we're going to have here is negative v0 equal to v0 because if you recall negative v0 is v final here plus one sixth g times t on the moon.
04:14
So we will separate this again and we'll have negative 2v not is equal to 1 6g times tm.
04:26
And let's, we can divide by one sixth g.
04:33
So what we're going to get is six times negative 2 v0 divided by g is equal to tm, which implies that time that the ball is in flight on the moon is going to be equal to six times the time that the ball is in flight on the earth.
04:55
But we would like to know how much further the ball travels.
04:59
And so for the x direction, on the earth, the ball in the horizontal direction, its velocity isn't changing...