A rocket is launched at an angle of 53.0° above the horizontal with an initial speed of 100 m/s.&nbsp;The rocket moves for 3.00 s along its initial line of motion with an acceleration of 30.0 m/s2. At&nbsp;this time, its engines fail and the rocket proceeds to move as a projectile. Find (a) the maximum&nbsp;altitude reached by the rocket, (b) its total time of flight, and (c) its horizontal range.

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A rocket is launched at an angle of 53.0° above the horizontal with an initial speed of 100 m/s.&amp;nbsp;The rocket moves for 3.00 s along its initial line of motion with an acceleration of 30.0 m/s2. At&amp;nbsp;this time, its engines fail and the rocket proceeds to move as a projectile. Find (a) the maximum&amp;nbsp;altitude reached by the rocket, (b) its total time of flight, and (c) its horizontal range.

user_27qwe · Accepted Answer

Given information:- Launch angle (θ) = 53.0°- Initial speed (v0) = 100 m/s- Acceleration (a) = 30.0 m/s2- Time along initial line of motion (t1) = 3.00 s(a) To find the maximum altitude reached by the rocket, we need to determine the vertical component of its motion. We can calculate the maximum height using the following formula:h=(v0sin(θ)2g)(v0sin(θ)+(v0sin(θ))2+2gh)where g is the acceleration due to gravity.Let&#039;s substitute the given values into the formula:h=(100sin(53.0°)2·9.8)(100sin(53.0°)+(100sin(53.0°))2+2·9.8·h)Simplifying this equation will give us the value of h, which represents the maximum altitude reached by the rocket.(b) To find the total time of flight, we need to consider the vertical motion of the rocket. The time of flight (T) can be calculated using the following formula:T=2v0sin(θ)gSubstituting the given values, we can find the total time of flight.(c) To find the horizontal range, we need to consider the horizontal motion of the rocket. The horizontal range (R) can be calculated using the formula:R=v0cos(θ)·TSubstituting the given values and the calculated value of T, we can find the horizontal range.

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