- #1

Toranc3

- 189

- 0

## Homework Statement

Suppose you are climbing in the high sierra when 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 s later, hear the sound of it hitting the ground at the foot of the cliff.

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

b) Suppose you had ignored the time it takes the sound to reach you. In that case, would you have overestimated or underestimated the height of the cliff? Explan your reasoning.

## Homework Equations

y=yo+vo*t+1/2*a*t^(2)

-b +or- [Sqrt(b^(2)-4ac)]/2a

## The Attempt at a Solution

t1=time for the rock to fall to the ground.

t2=time for the sounds to go from bottom to top of cliff

t1+t2=10seconds

**For rock falling down:**

y=yo+vo*t+1/2*a*t^(2)

0=H-4.905m/s^(2)*t1^(2)

**For sound coming up from the bottom:**

y=yo+vo*t+1/2*a*t^(2)

H=330m/s*t2 - 4.905m/s^(2)*t2^(2)

substitute t2 with (10seconds-t1) and then equate the equations from sound and rock.

4.90m/s^(2)*t1^(2)=330m/s(10s-t1)-4.905m/s^(2)(10s-t1)^(2)

I end up with 9.81m/s^(2)*t1^(2) + 231.9m/s*t1-2809.5m

I use the quadratic formula to get this

t1=8.8224 seconds

I end up with H=381.7850m.

I do not get part b though.

## Homework Statement

## Homework Equations

## The Attempt at a Solution

Last edited: