Physics Cliffs Question

Question

You slide down an avalanche from a height of 20 meters. Once you reach the bottom of the avalanche, you have the misfortune of flying of a 15 meter cliff horizontally. How far from the base do you land? Neglect friction.

Answer 1

Potential Energy at the top of the avalanche is mgh = (9.81)(20)m and then assuming no lost energy to work in the slide down means all potential energy was converted to kinetic energy meaning:

(9.81)(20)m = 1/2mv²

(where v is the horizontal velocity)

2(9.81)(20) = v²

v = √(2•9.81•20) = 19.81 m/s

The time it takes to hit the ground from 15 meters is calculated from:

x = 1/2gt²

15 = (1/2)(9.81)t²

(2)(15)/9.81 = t²

t = √(2•15/9.81) = 1.7496 seconds

During that 1.7496 seconds, while traveling horizontally at 19.81 m/s, you travel 1.7496•19.81 or approx 35 meters from the base of the cliff.