A rock is dropped from a sea cliff and the sound of it striking the ocean is heard 3.7 s later. If the speed of sound is 340 m/s, how high in meters is the cliff?
Let H be the height of the cliff. The time to hear the sound of hitting the water is
t = t1 + t2, where t1 is the time it takes to hit the water and t2 is the additional time for the sound to arrive at the top of the cliff.
H - (1/2) g t1^2
t1 = sqrt (2H/g)
t2 = H/V
where V is the speed of sound in air. (Look it up).
Solve t1 + t2 = 3.7 for H
A rock is dropped from a sea cliff, and the sound of it striking the ocean is heard 3.1s later.
To find the height of the cliff, first, we need to determine the time it took for the rock to fall. We can do this by subtracting the time it took for the sound to reach us after the rock struck the water from the total time it took for us to hear it.
Let's call the time it took for the rock to fall "t_fall" and the time it took for the sound to travel "t_sound".
Given:
t_sound = 3.7 s
Speed of sound = 340 m/s
The time taken for the rock to fall can be calculated as:
t_fall = t_sound - t_sound
t_fall = 3.7 s - 0 s
t_fall = 3.7 s
Now, using the equation of motion:
h = (1/2) * g * t_fall^2
where:
h = height of the cliff
g = acceleration due to gravity (approximately 9.8 m/s^2)
t_fall = time taken for the rock to fall
Substituting the known values, we get:
h = (1/2) * 9.8 m/s^2 * (3.7 s)^2
h ≈ 1/2 * 9.8 m/s^2 * 13.69 s^2
h ≈ 67.4 m
Therefore, the height of the cliff is approximately 67.4 meters.
To determine the height of the cliff, we'll need to consider the time it takes for the sound to travel back up from the point of impact to the top of the cliff.
Let's break down the problem step by step:
1. Calculate the time it took for the rock to fall until it hit the water.
Since the sound is heard 3.7 seconds later, it means this is the total time it took for both the rock to fall and the sound to travel back up to the top of the cliff.
2. The speed of sound is given as 340 m/s, so we can use this value to calculate the distance traveled by sound during the 3.7 seconds it took to hear it.
Distance = Speed * Time
Distance = 340 m/s * 3.7 s
3. Now, we need to consider the time it took for the rock to fall. This is the time it took for the sound to travel back up, which we just calculated. So, to determine the time it took for the rock to fall until it hit the water, we can subtract this time from the total time of 3.7 seconds.
Time for rock to fall = Total time - Time for sound to travel back up
Time for rock to fall = 3.7 s - (distance/speed)
4. Next, we can calculate the distance fallen by the rock using the equation for free fall:
Distance = (1/2) * g * t^2
where g is the acceleration due to gravity (approximately 9.8 m/s^2) and t is the time for the rock to fall (which we calculated in the previous step).
5. Finally, we have the distance fallen by the rock, which is the same as the height of the cliff.
Let's calculate it:
Step 1:
Total time = 3.7 s
Step 2:
Distance = 340 m/s * 3.7 s = 1258 m
Step 3:
Time for rock to fall = 3.7 s - (1258 m / 340 m/s) = 3.7 s - 3.70 s = 0 s
Step 4:
Distance = (1/2) * 9.8 m/s^2 * (0 s)^2 = 0 m
Step 5:
The height of the cliff is 0 meters.
Therefore, the cliff has a height of 0 meters, which means the rock didn't actually have time to fall before hitting the water.