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A rocket is fired upward from the earth's surface such that it creates an acceleration of 19.6 m/sec2. If after 5 sec its engine is switched off, the maximum height of the rocket from earth's surface would be

Question

A rocket is fired upward from the earth's surface such that it creates an acceleration of 19.6 m/sec2. If after 5 sec its engine is switched off, the maximum height of the rocket from earth's surface would be

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Solution

To solve this problem, we need to use the equations of motion.

Step 1: Calculate the final velocity when the engine stops We know that the initial velocity (u) is 0 (as the rocket starts from rest), the acceleration (a) is 19.6 m/s², and the time (t) is 5 seconds. We can use the first equation of motion to find the final velocity (v):

v = u + at v = 0 + (19.6 m/s² * 5 s) v = 98 m/s

Step 2: Calculate the maximum height After the engine is switched off, the rocket will continue to ascend but now under the influence of gravity alone (which we'll take as -9.8 m/s²). It will decelerate until its velocity is 0, at which point it will have reached its maximum height. We can use the second equation of motion to find this height (h):

v² = u² + 2as 0 = (98 m/s)² + 2*(-9.8 m/s²)*s 0 = 9604 m²/s² - 19.6 m/s² * s 9604 m²/s² = 19.6 m/s² * s s = 9604 m²/s² / 19.6 m/s² s = 490 m

So, the maximum height of the rocket from the earth's surface would be 490 meters.

This problem has been solved

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