Question

Free Fall On the moon, the acceleration due to gravity is 1.6 m/sec².

(a) If a rock is dropped into a crevasse, how fast will it be going just before it hits bottom 30 sec later?

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(b) How far below the point of release is the bottom of the crevasse?

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(c) If instead of being released from rest, the rock is thrown into the crevasse from the same point with a downward velocity of 4 m/sec, when will it hit the bottom and how fast will it be going when it does?

Answer 1

Given that data: on the moon, the acceleration due to gravity is

(a) We have to find the fast will it be going just before it hits bottom if a rock is dropped into a crevasse.

Since acceleration is the derivative of the velocity.

Since given that

Taking integration on both sides, with respect to t we have

And

Therefore, put,

The rock will be going 48 m/sec.

(b) Let represent position and it is the anti derivative of velocity.

Since

Taking integration on both sides, with respect to t we have

But

Therefore,

The rock travels 720 meters in the 30 seconds it takes to the hit bottom of the crevasse is 720 meters below the point of release.

(c) Released from rest that means

The velocity is now given by where (note that the sign of the initial velocity is the same as the sign used for the acceleration, since both act in a downward direction.)

Therefore, and

Where and so.

Using and the known crevasse depth of 720 meters,

We solve to obtain the positive solution and

So

The rock will hit be going about