Acatapult launches a rocket at an angle of 53.0° above the horizontal with an initial speed of 100 m/s. the rocket engine immediately starts a burn, and for 3.00 s the rocket moves along its initial line of motion with an acceleration of 30.0 m/s2. then its engine fails, and the rocket proceeds to move in free fall. find (a) the maxi- mum altitude reached by the rocket, (b) its total time of flight, and (c) its horizontal range.

Explanation:

A catapult launches a rocket at an angle of 53.0° above the horrizontal,

with an initial speed of 100m/s

The rocket engine immediately starts a burn, and for 3.00 s;  the rocket moves allong its initial line of motion with an acceleration of 30.0 m/s²

Then its engine fails and the rocket proceeds to move in free fall.

(a) We are first to find the maximum altitude reached by the rocket:

Final velocity (v) = acceleration × time = 30m/s² × 3.00 s = 90 m/s

The initial velocity (u) is 100m/s

Average velocity = = = 95 m/s

Displacement = average velocity × time taken = 95m/s × 3.00 s = 285 m

(b) We are then to find total time of flight.

The initial velocity when the catapult is starting to fall is 90 m/s

The final velocity of the catapult = 0 m/s

Average velocity = = = 45 m/s

Time taken to fall = average velocity ÷ gravitational acceleration (9.8 m/s²) = 45 m/s ÷ 9.8 m/s² = 4.591836735 seconds = 4.59 s (to nearest two decimal places)

Total time taken = 3.00 s + 4.59 s = 7.59 s

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