A rock is projected upward from the surface of the moon y=0, at t=0 with a...

A rock is projected upward from the surface of the moon y=0, at t=0 with a velocity of 30m/s(j). The acceleration due to gravity at the surface of the moon is -1.62m/s^2(j). When will the rock have a speed of 8.0 m/s?

Expert Solution

There will be two such times when the speed of the rock will be 8 m/s.One will be along the upward path of the rock and the second will be along the returning downward motion of the rock.

1) During upward motion , we can write - v = u + a*t

=> 8 = 30 - 1.62 * t1

=> t1 = 13.58s.

2) Now let us calculate the time when the speed of the rock becomes 0. For this using the same equation of motion as before :-

v = u + a*t

=> 0 = 30 - 1.62 * t2

=>t2 =18.51 s.

Now after this the rock will have downward motion with acceleration 1.62m/s^2. Let us check when the speed of the rock becomes 8 m/s for the second time :-

v = u + a*t

=>8 = 0 + 1.62 * t3

=>t3 = 4.938s

Therefore the total time for the rock to have a speed of 8 m/s from the beginning ( at t=0 ) becomes t2 + t3 = 18.51s + 4.94s = 23.45.

So the rock has a speed of 8 m/s at 13.58s and 23.45s.

genius_generous answered 2 days ago

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A rock is projected upward from the surface of the moon y=0, at t=0 with a...

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Expert Solution

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