To estimate how high the cliff is you throw a rock off the edge and 7.8 s later you hear the rock hit the ground. The speed of sound is 330 m/s. Ignoring air resistance how high is the cliff?
h = (1/2)(9.81)(tfall)^2
h = 330 (7.8-tfall)
660 (7.8-tfall) = 9.81 tfall^2
9.81 tf^2 + 660 tf - 5148 = 0
for the positive root I get 7.06
so the sound comes up for
7.8 - 7.06 = .7407 seconds
.7404*330 = 244 meters
To determine the height of the cliff, we need to calculate the time it takes for the rock to fall. Assuming the only significant force acting on the rock is gravity, we can use the kinematic equation for vertical motion:
h = 1/2 * g * t^2
Where:
h is the height of the cliff
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time it takes for the rock to fall
In this scenario, the time for the rock to fall is the time it takes for the sound of the impact to travel back to your ears. Since the speed of sound is given as 330 m/s, and it takes 7.8 seconds for the sound to reach you, the total time for the rock to fall is twice that time (since it takes the same amount of time for the sound to travel back to you):
t = 2 * 7.8 s = 15.6 s
Now we can plug this value of time into the equation to calculate the height of the cliff:
h = 1/2 * g * t^2
h = 1/2 * 9.8 m/s^2 * (15.6 s)^2
h = 1/2 * 9.8 m/s^2 * 243.36 s^2
h ≈ 1196.7 m
Therefore, the estimated height of the cliff is approximately 1196.7 meters.