Question

If you drop a 5kg rock down a 20 m well, how fast will it be traveling when it hits the ground

Answer 1

The final speed of the rock is 19.8 m/s

Explanation:

We can solve this problem by using the law of conservation of energy: the total mechanical energy of the rock (the sum of potential energy + kinetic energy) must be conserved during the fall. Therefore we can write:

$U_i +K_i = U_f + K_f$

where :

$U_i$ is the initial potential energy, at the top

$K_i$ is the initial kinetic energy, at the top

$U_f$ is the final potential energy, at the bottom

$K_f$ is the final kinetic energy, at the bottom

We can rewrite the equation as:

$mgh_i + \frac{1}{2}mu^2 = mgh_f + \frac{1}{2}mv^2$

where:

m = 5 kg is the mass of the rock

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

$h_i = 20 m$ is the initial height  of the rock

u = 0 is the initial speed

$h_f = 0$ since the rock falls to the ground

v is the final speed

And solving for v, we find the final speed:

$v=\sqrt{2gh_i}=\sqrt{2(9.8)(20)}=19.8 m/s$

Learn more about kinetic energy and potential energy:

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