How High is the Cliff if You Hear the Rock Hit After 7 Seconds?

[devxx]

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 7.00 s later, hear the sound of it hitting the ground at the foot of the cliff.

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

Homework Equations

V(final)= V(initial)- g
y(final) = y (initial) +Vi(t) - .5 g(t^2)
(Vf)^2=(Vi)^2 - 2g (Yf-Yi)

The Attempt at a Solution

330 = Yi + 0(7) - .5 (9.8)(700)^2
I'm really having trouble just getting past the first part. It seems like it should be pretty straight forward but I'm probably over thinking it.

 

[Anden]

You should try to get two equations: One for the distance traveled by the rock with respect to time, and one for the distance traveled by the sound with respect to time. When you have these you can combine them and get the answer (You will need to rearrange the terms in the equations)

 

[tomcue]

I would approach this problem by first identifying the known values and the equations that can be used to solve for the unknown value, which in this case is the height of the cliff. The known values are: the speed of sound (330 m/s), the time it takes for the sound to reach the bottom of the cliff (7.00 s), and the acceleration due to gravity (9.8 m/s^2).

Using the equation V(final) = V(initial) + at, we can calculate the initial velocity of the rock when it was dropped from the top of the cliff. Since the rock was dropped, the initial velocity (Vi) is equal to 0. Therefore, we can rewrite the equation as V(final) = at.

Next, we can use the equation y(final) = y(initial) + Vi(t) - 0.5gt^2 to calculate the height of the cliff. Again, we can substitute 0 for the initial velocity (Vi) and the value of acceleration due to gravity (g) is -9.8 m/s^2 since it acts in the opposite direction of the rock's motion.

Plugging in the known values, we get y(final) = 0 + 0(7) - 0.5(-9.8)(7)^2 = 240.1 m. Therefore, the height of the cliff is approximately 240.1 meters.

However, it is important to note that this calculation is only accurate if we ignore air resistance. In reality, air resistance would affect the time it takes for the sound to reach the bottom of the cliff and therefore, the calculated height may not be entirely accurate. To account for air resistance, we would need more information such as the density and viscosity of the air in the foggy conditions.