A rocket is fired vertically from theground. It moves upwards with aconstant acceleration of 10 𝑚/𝑠2. After30 seconds the fuel is finished. Afterwhat time from the instant of firing therocket will it attain the maximumheight? 𝑔 = 10 𝑚 /𝑠2:
Question
A rocket is fired vertically from theground. It moves upwards with aconstant acceleration of 10 𝑚/𝑠2. After30 seconds the fuel is finished. Afterwhat time from the instant of firing therocket will it attain the maximumheight? 𝑔 = 10 𝑚 /𝑠2:
Solution
The problem can be divided into two parts:
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The time it takes for the rocket to ascend with constant acceleration.
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The time it takes for the rocket to descend under the force of gravity.
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The rocket ascends with a constant acceleration of 10 m/s² for 30 seconds. The final velocity (Vf) at the end of this period can be calculated using the equation of motion: Vf = Vi + at, where Vi is the initial velocity, a is the acceleration, and t is the time. Since the rocket starts from rest, Vi = 0. So, Vf = 0 + 10*30 = 300 m/s.
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After the fuel is finished, the rocket will continue to ascend until its velocity becomes zero, at which point it will start to descend. The time it takes for the velocity to become zero can be calculated using the equation Vf = Vi - gt, where Vi is the initial velocity, g is the acceleration due to gravity, and t is the time. Setting Vf = 0, we get 0 = 300 - 10*t, which gives t = 300/10 = 30 seconds.
So, the total time from the instant of firing the rocket until it attains the maximum height is 30 (ascent with acceleration) + 30 (ascent without acceleration) = 60 seconds.
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