Why Is My Calculation on Rocket's Projectile Motion Incorrect?

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The discussion centers on the calculation of a rocket's projectile motion, specifically addressing issues with determining its maximum altitude, total time of flight, and horizontal range after an initial powered ascent. The rocket is launched at a 53° angle with a speed of 75 m/s and accelerates at 21 m/s² for 21 seconds before its engines fail. Despite following the teacher's instructions, the calculations yield incorrect results, prompting a need for clarification on the application of projectile motion principles. Key factors include the transition from powered flight to free fall and the correct use of kinematic equations. Accurate calculations are essential for understanding the rocket's trajectory and performance.
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this is vectors and projectiles...our teacher told us how to do it...and i did exactly what he told us to do, but it isn't right...

A rocket is launched at an angle of 53° above the horizontal with an initial speed of 75 m/s, as shown in Figure 3-31. It moves for 21 s along its initial line of motion with an acceleration of 21 m/s2. At this time its engines fail and the rocket proceeds to move as a free body.

(a) What is the rocket's maximum altitude?

(b) What is the rocket's total time of flight?

(c) What is the rocket's horizontal range?
 
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