On the moon, the acceleration due to gravity is -1.6 meters per second per second. A stone is dropped from a cliff on the moon and hits the surface of the moon 20 seconds later.
a)How far did it fall?
h = h0 + v0t + at2
When the stone is dropped, the height above the moon's surface is
h0. That is the unknown we want to find.
Since the stone is merely dropped, not thrown down, v0 = 0.
After t = 20 seconds, the height above the moon's surface is h = 0.
Substituting these, along with a = -1.6
0 = h0 + (0)t + (-1.6)(20)2
Simplifying:
0 = h0 - 320
Solving that gives:
h0 = 320 meters.
b)What was its velocity at impact?
We use the formula which is the derivative of
the formula used in part (a), namely
v = v0 + at
v = 0 + (-1.6)(20)
v = -32
The reason the velocity is negative is because the stone
is going downward.
Edwin