Solving Symbolically: Height of Cliff with No Air Resistance

[SavannahN]

Homework Statement

You are climbing in the High Sierra when you suddenly find yourself at the edge of a fogshrouded
cliff. To find the height of this cliff, you drop a rock from the top; a time T later you
hear the sound of the rock hitting the ground at the foot of the cliff.

a. If you ignore air resistance, how high is the cliff if the speed of sound is v_s?

Homework Equations

s = v * t
s =1/2*a*t²

The Attempt at a Solution

h = ¹/₂*g*t_rock² (rock)
h = t_sound *v_s (sound)
​

T = t_sound + t_rock
-> t_sound = T - t_rock​

h = (T - t_rock)*v_s
​

h = ¹/₂*g*t_rock²​

-> t_rock = root(2*h/g)​

​

h = (T - root(2*h/g))*v_s

after this I am lost in separating the h, so I am assuming that I did something wrong. Where did I go wrong?

 

[kuruman]

after this I am lost in separating the h, so I am assuming that I did something wrong. Where did I go wrong?

Your expression is correct. To find the height, just square both sides and solve the quadratic. Be sure you pick the right solution of the two as your answer.