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Answer :
Final answer:
The problem requires finding the total time of flight for a rocket that undergoes powered flight, followed by unpowered ascent and descent in a parabolic path. Calculation involves finding the initial vertical velocity and using it to determine the time to peak and then doubling for a symmetrical return path.
Explanation:
The question involves calculating the time of flight for a rocket that is launched from rest and accelerates at a constant rate until engine cutoff, after which it follows a parabolic path due to gravity. To find the total flight time, we must determine the flight duration during the powered ascent and the subsequent unpowered descent.
During the powered flight, which lasts for 18 seconds, the rocket accelerates at 35.0 m/s² at a 27.5° angle above the horizontal. This initial phase will give the rocket both horizontal and vertical velocity components. Once the engines shut off, the rocket will be subject only to the force of gravity, causing it to ascend until its vertical velocity component is zero, and then fall back to the ground. The time taken to rise to the peak and then fall back will be symmetrical due to the parabolic nature of the trajectory.
To find the duration of the unpowered flight, we'll need to calculate the vertical component of the velocity at engine cutoff and use it to determine the time taken to reach the peak of the ascent. From there, we can use symmetry to infer that the descent time from the peak back to the ground is equal to the ascent time. Adding the time of powered flight and the time of unpowered flight will give us the total flight time.
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