Question

If a rock climber accidentally drops a 77.5-g piton from a height of 215 meters, what would its speed be just before striking the ground? ignore the effects of air resistance.

Answer 1

Let us list out what we know from the question.

Initial Velocity $V_{i} = 0$ since the piton is 'dropped'.

Vertical Displacement of the piton D = 215 m

Acceleration due to gravity $a = 9.8 m/s^{2}$

Final Velocity $V_{f} = ?$

Using the equation, $V^{2} _{f} = V^{2} _{i} + 2aD$ and plugging in the known values, we get

$V^{2} _{f} = 0^{2} + 2(9.8)(215)$

Simplifying by taking square-root on both sides gives us $V_{f} = 64.915 m/s$

Thus, the speed of the piton just before striking the ground is 65 m/s.