A rock is dropped from a sea cliff and the sound of it striking the ocean is heard 5.2 seconds later. If the speed of sound is 340 m/s, how high is the cliff?
distance = rate * time
height = 5.2 * 340 = 1768m
It should be as simple as that.
The time given is the time of falling and the time of thesound going up.
time sound= h*340
time falling
h= 1/2 g timefalling or
time falling= 2h/g=5.2-h*340 solve for h
Michael, the time given is not the time for the sound traveling. See my post
Oh, sorry. I didn't mean to give wrong information.
Bob - is "g" in your equation gravity?
g is the acceleration due to gravity, yes.
To determine the height of the cliff, we can use the formula for the distance traveled by an object in free fall:
d = 0.5 * g * t^2
Where:
- d is the distance traveled (the height of the cliff)
- g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth)
- t is the time it takes for the rock to fall
In this case, we need to find the time it takes for the rock to hit the ocean. We know that the sound is heard 5.2 seconds after the rock is dropped. However, sound travels at a speed of 340 m/s, so there will be a delay between the rock hitting the ocean and the sound reaching us.
To find the actual time it takes for the rock to fall, we subtract this delay from the time measured:
actual_time = measured_time - delay
The delay can be calculated using the speed of sound and the distance traveled by sound in the given time. Since the rock is dropped from the cliff, we can assume that the sound's distance traveled is the same as the rock's initial height.
Now, let's calculate the delay:
delay = distance / speed
Since the distance traveled by sound is equal to the height of the cliff, and the speed of sound is 340 m/s, we have:
delay = height / 340
Substituting this into the equation for actual_time, we have:
actual_time = measured_time - (height / 340)
Plugging in the values, we get:
5.2 = actual_time - (height / 340)
Rearranging the equation, we have:
actual_time = 5.2 + (height / 340)
Now, substitute this value of actual_time back into the equation for the distance traveled by the rock:
height = 0.5 * g * (actual_time)^2
Plugging in the values, we get:
height = 0.5 * (9.8) * (5.2 + (height / 340))^2
Now, we solve this equation to find the height of the cliff. This is a little more complex because the height appears on both sides of the equation. To simplify it, we first square the term (5.2 + (height / 340))^2:
height = 0.5 * (9.8) * (27.04 + 0.0304 * height + 2 * height / 340)
Simplifying further:
height = 0.5 * (9.8) * (27.04) + 0.5 * (9.8) * (0.0304 * height + 2 * height / 340)
height = 132.352 + 0.1472 * height + 0.28 * height / 340
Combining like terms:
height - 0.1472 * height - 0.28 * height / 340 = 132.352
Simplifying further:
(1 - 0.1472 - 0.28 / 340) * height = 132.352
(1 - 0.1472 - 0.000823529) * height = 132.352
Calculating the value in parentheses:
0.852976471 * height = 132.352
Solving for height:
height = 132.352 / 0.852976471 ≈ 155.17 meters
Therefore, the height of the cliff is approximately 155.17 meters.