Find Cliff Height | Physics Homework

[Toranc3]

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

 

[tms]

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/*a*t^(2)

-b+- Sqrt(B^(2)-4ac)/2a

Be careful with how you write the equations. Neither of these is correct.

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

This is also not correct.

For rock falling down:

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

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

When working problems, it is always best to solve the problem symbolically, and only plug in numbers at the very end. One problem with plugging in numbers in the beginning is that you force your readers to figure out what the numbers are and where they come from.

For sound coming up from the bottom:

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

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

Why the second term on the right?

I do not get part b though.

What don't you get about it?

 

[rude man]

Sound is not subject to gravity!

 

[Toranc3]

So for sound 1/2*a*t^(2) should go to zero right? Got it thanks guys!