A rocket, starting from rest, travels straight up with an acceleration of 65.0 m

Question

A rocket, starting from rest, travels straight up with an acceleration of 65.0 m/s2. When the rocket is at a height of 412 m, it produces a sound that eventually reaches a ground-based monitoring station directly below. The sound is emitted uniformly in all directions. The monitoring station measures a sound intensity I. Later, the station measures an intensity one-third I. Assuming that the speed of sound is 343 m/s, find the time that has elapsed between the two measurements.

A rocket, starting from rest, travels straight up with an acceleration of 65.0 m/s2. When the rocket is at a height of 412 m, it produces a sound that eventually reaches a ground - based monitoring station directly below. The sound is emitted uniformly in all directions. The monitoring station measures a sound intensity I. Later, the station measures an intensity one - third I. Assuming that the speed of sound is 343 m/s, find the time that has elapsed between the two measurements.

Explanation / Answer

A rocket, starting from rest, travels straight up with an acceleration of 58.0 m/s2. When the rocket is at a height of 562 m, it produces sound that eventually reaches a ground-based
monitoring station directly below. The sound is emitted uni-formly in all directions. The monitoring station measures a soundintensity I. Later, the station measures an intensity 1/3 I. Assuming
that the speed of sound is 343 m/s, find the time that has elapsed between the two measurements.

Alright so first you want to solve for the time in which the rocket reaches 562 m. You have acceleration, distance, and velocity initial (since it is at rest, it is assumed to be 0).
With these variables, you can use the equation: d=Vo(t) + 1/2(at^2)
Since Vo = 0, Vo(t) = 0 (multiplying by 0 = 0)
Therefore d=1/2(at^2)
rearrange for t:
Square root(2d/a)=t, solve for t
t=4.40s

Now from the height of 562, do the calculation for the time required for the sound to reach the monitoring station. You are given distance and velocity (Since velocity is uniform, you can use v=d/t).
Rearrange for t:
t=d/v
t=1.64s

Now i am not entirely sure what the question is asking (as in time elapsed between the two measurements). If you have answers you can verify what to do with time, but i assume it means the time it takes for the 2nd reading. Therefore, you just add the two times (since one is the time it takes for the rocket to go 562m in the air, and the other is the time it takes for the speed of sound to reach the monitoring station)

So: 1.64s + 4.40s = 6.04s

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