How tall is the cliff?

Question

A physics teacher performing an outdoor demonstration suddenly falls from rest off a high cliff and simultaneously shouts "Help". When she has fallen for 3.0 s , she hears the echo of her shout from the valley floor below. The speed of sound is 340 m/s

1.Find how tall is the cliff?

2.If air resistance is neglected, how fast will she be moving just before she hits the ground? (Her actual speed will be less than this, due to air resistance.)

Answer 1

Make some variables:

Let:

"h" be the height of the cliff;

"d" be the distance she falls when she hears the echo.

"s" be the total distance the sound travels (down & back up).

First, we can figure out "s" (or at least rewrite it):

The sound goes down distance "h" (all the way to the bottom);

Then it comes back up a distance of "h-d" (where it meets the teacher).

So the total distance the sound travels is:

s = h + (h-d) = 2h - d

> "When she has fallen for 3.0 s ..."

We can calculate how far she falls in 3 seconds using this gravity formula:

d = ½gt²

= ½(9.8m/s²)(3 sec)²

= 44.1 meters

Combine with equation for "s":

s = 2h - d = 2h - 44.1m

> "The speed of sound is 340 m/s"

And we know the sound traveled for 3 seconds and went distance "s", so:

s = (340 m/s)(3 sec) = 1020 meters

Combine with previous equation:

2h - 44.1m = 1020m

Now just solve for "h".

> how fast will she be moving just before she hits the ground?

Use the formula:

v = sqrt(2gh)