A rock is dropped from a sea cliff and the sound of it striking the ocean is heard 6.4 s later. If the speed of sound is 340 m/s, how high is the cliff?
The time of 6.4 s is the sum of the time required for the rock to hit the sea, sqrt (2H/g), and the time for the sound to get back, (H/V).
H = cliff height
V = speed of sound
g = acceleration of gravity
Solve this equation for H:
6.4 = H/340 + sqrt(H/4.9)
That can be turned into a quadratic equation. Only one root will be positive.
172.35
356.8
To determine the height of the cliff, we can use the equation for the distance traveled by an object under constant acceleration:
d = v0t + (1/2)at^2
In this case, the initial velocity (v0) of the rock when it is dropped is 0 m/s because it is not given an initial upward or downward push. The acceleration (a) due to gravity is approximately 9.8 m/s^2 (assuming no air resistance). And the time it takes for the sound to travel to the ocean and back to your ears is 6.4 seconds.
First, let's calculate the distance traveled by the sound from the ocean to your ears.
Using the formula:
distance = speed × time
distance = 340 m/s × 6.4 s
distance = 2176 m
Since the sound has traveled 2176 m in each direction (ocean to ears and ears to ocean), we only need to consider the time it takes for the sound to reach your ears.
Now, let's calculate the time it takes for the rock to fall to the ocean:
6.4 s - 2 × (time for sound to travel) = time for rock to fall
2 × (time for sound to travel) is used because the sound has to travel from the ocean to your ears and then back again to the ocean.
6.4 s - 2 × (distance / speed) = time for rock to fall
6.4 s - 2 × (2176 m / 340 m/s) = time for rock to fall
6.4 s - 12.8 s = time for rock to fall
-6.4 s = time for rock to fall
This is not possible because time cannot be negative in this context. It means that the time for the rock to fall is less than the time it takes for the sound to travel.
Therefore, there seems to be an error in the problem statement, and we cannot determine the height of the cliff with the given information.