A rock is dropped from a sea cliff 400m high.If the speed of sound is a constant 330 m/s, how long after the rock is dropped is the sound of the splash heard at the top of the cliff?
break the total sound into two parts:
1) time for the rock to hit the surface.
h=ho-4.9t^2
t= sqrt(400/4.9) check that.
2) time for the sound to go 400m
t= 400/343
check that
add the two times.
^acceleration is 9.8 as well. and wheres 343 from ?
Shut up
i tihnk that's a typo
To find out how long after the rock is dropped the sound of the splash is heard at the top of the cliff, we need to calculate the time it takes for the rock to fall to the water and then the time it takes for the sound to travel back to the top of the cliff.
1. Calculate the time it takes for the rock to fall:
We can use the formula for free fall:
s = ut + (1/2)at²
Here, s is the distance the rock falls (400m), u is the initial velocity (0 m/s as the rock is dropped), a is the acceleration due to gravity (-9.8 m/s²), and t is the time it takes for the rock to reach the water.
Plugging in the values, we have:
400 = 0 + (1/2)(-9.8)t²
Solving for t, we get:
400 = -4.9t²
t² = 400/-4.9
t ≈ 8.16 seconds
Therefore, it takes approximately 8.16 seconds for the rock to fall to the water.
2. Calculate the time it takes for the sound to travel back up:
The speed of sound is given as a constant 330 m/s.
Since the sound has to travel a distance of 400m down to the water and then 400m back up to the top of the cliff, the total distance traveled by the sound is 800m.
Time = Distance / Speed
t = 800 / 330
t ≈ 2.42 seconds
Therefore, it takes approximately 2.42 seconds for the sound to travel back up to the top of the cliff.
3. Add the time for the rock to fall and the time for the sound to travel back up:
t_total = t_rock_fall + t_sound_travel
t_total = 8.16 + 2.42
t_total ≈ 10.58 seconds
Therefore, the sound of the splash is heard at the top of the cliff approximately 10.58 seconds after the rock is dropped.