How Can You Calculate Cliff Height Using Sound?

[babbagee]

here is the question

Cliff Height. You are climbing in the High Sierra where you suddenly find yourself at the edge of a fog-shrouded cliff. To find the height of this cliff, you drop a rock from the top and 10.0 s later hear the sound of it hitting the ground at the foot of the cliff.

Ignoring air resistance, how high is the cliff if the speed of sound is 330 m/s

ok i did the problem and i just wanted at least to people to check my work.


h = .5gt²

time for sound to reach the person
t_s = h/v_sound


since the total time is ten seconds then i can solve both equations for time
time for rock to hit ground
t = sqrt(2h/g)
time for sound to travel up to the person
t = h/v_sound

then t_total = sqrt(2h/g) + h/v_sound

then i can solve for h.

I got -1086.9m and -14130.43m

can at least two people confirm that. The reason i am asking is because I am doing my homework online and i have one more try to get it right, so i want to make sure I got it right.

Thanks

 

[Fermat]

Check your arithmetic for the quadratic.

The answer is closer to 380 m - which you can check by substituting it into the expression you already had - t_total = sqrt(2h/g) + h/v_sound - it's correct.