On the apollo 14 mission to the moon astronaut alan shepard...

On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a golf club improvised from a tool. The free-fall acceleration on the moon is 1/6 of its value on earth. Suppose he hit the ball with a speed of 35 m/s at an angle 36° above the horizontal. How long was the ball in flight? Express your answer to two significant figures and include the appropriate units. How far did it travel? Express your answer to two significant figures and include the appropriate units. Ignoring air resistance, how much farther would it travel on the moon than on earth? Express your answer to two significant figures and include the appropriate units.

Transcript

00:01 Okay, so we have a golf ball on the moon, starting with a velocity of 35 meters per second, and being hit up at an angle of 36 degrees.

00:17 And so the first part asks us to find how long it is up in the air, so how long it takes for it gets back to the ground.

00:27 So let's just look and see what we have here in this problem.

00:33 So they're telling us that the acceleration due to gravity, which is going to be our acceleration in the y direction, is equal to one -sixth of the gravity on earth.

00:54 So that's going to be 9 .81 meters per second squared divided by six.

01:04 And so that is negative.

01:07 It's pulling downward.

01:09 And you end up with 1 .64 meters per second squared for our acceleration.

01:19 And then there's just, there's no acceleration in the x direction.

01:23 All we've got is the gravity here.

01:27 So nothing there.

01:29 We have our initial velocity, and we can break that up into the component's initial velocity in x and y directions.

01:39 So we've got 36 degrees.

01:43 We just have to find our x and our y components.

01:50 So we've got our angle here, and then we just got to do anything about the adjacent side.

01:59 Just this bottom part here, that's the x, and then the side that is across from the angle.

02:06 So the opposite, that's going to be sign.

02:08 So vx is going to be 35 meters per second times cosine of 36 degrees.

02:27 Vi .y is 35 times sine, 36 degrees.

02:34 And if we put that in our calculator, now we get 28 .32 meters.

02:46 Per second and 20 .57.

03:01 Ok.

03:04 Now we want to know the final time.

03:07 So that total time elapsed when it hits the ground.

03:13 So at that point here, our initial velocity, or actually our final velocity right before it hits there, in the y direction, is going to be equal to our initial velocity in the y direction, because it's at the same height, which is zero.

03:45 But it is in the opposite direction.

03:50 So it's going downward at that point instead of up.

03:56 So the v final in the y direction is the opposite of vi, the initial, in the y direction.

04:06 So we can use the equation vy final equals v .y, v...

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