Question

A physics teacher stands at the edge of a cliff at Canyonlands National Park. The teacher wants to know how high above the base of the cliff he is, so, making sure there are no hikers below drops a large rock over the edge of the cliff. 5.8 seconds after releasing the rock, the teacher hears the sound of the rock hitting the ground below. If sound can travel at a constant speed of 330 m/s, how high is the cliff?

Answer 1

Height = y
T = 5.8 sec
tf = time to fall
ts = time for sound to travel distance y

T = tf + ts = √[2y/g] + y/330
or
(T - y/330)² = 2y/g
a quadratic in y.
y = 141.4 m
hope this helps