Question

The wind blows a rock of mass m off a cliff. The rock hits the ground below with speed v. Then a rock of mass 2m is blown off the same cliff. It will hit the ground at what speed? Assume that air resistance is negligible for both rocks.

2v

0.5v

4v

v

Answer 1

The speed of the second rock is also v

Explanation:

The motion of the rock is a free fall motion: it is affected only by the force of gravity. Therefore, the rock accelerates towards the ground with a constant acceleration, $g=9.8 m/s^2$ downward (acceleration of gravity). Therefore the final velocity can be found using the suvat equation:

$v^2-u^2=2as$

where :

v is the final velocity

u is the initial velocity  (u = 0, since the initial vertical velocity of the rock is zero)

$a=g=9.8 m/s^2$ is the acceleration

s is the distance covered , which corresponds to the height of the cliff

Solving the equation for v,

$v=\sqrt{2as}$

We see that the value of v does not depend on the mass of the rock, but only on the height of the cliff, s: since the two rocks in the problem fall from the same height, they hit the ground with same speed.

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