Concept explainers
A catapult 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 maximum altitude reached by the rocket, (b) its total time of flight, and (c) its horizontal range.
(a)
The maximum altitude reached by the rocket.
Answer to Problem 4.65AP
The maximum altitude reached by the rocket is
Explanation of Solution
Given info: The initial speed of the rocket is
The formula to calculate the vertical height reached by the rocket is,
Here,
Substitute
Thus, the vertical height of rocket is
The speed of the rocket after the failure is,
Substitute
The height reached by the rocket after the engine failure is,
Here,
Substitute
The maximum height reached by the rocket is,
Substitute
Conclusion:
Therefore, the maximum altitude reached by the rocket is
(b)
The total time of flight of the rocket.
Answer to Problem 4.65AP
The total time of flight of the rocket is
Explanation of Solution
Given info: The initial speed of the rocket is
The vertical height reached by the rocket at the time of free fall is,
Here,
Substitute
The total time of the flight of the rocket is,
Substitute
Conclusion:
Therefore, the total time of flight of the rocket is
(c)
The horizontal range of the rocket.
Answer to Problem 4.65AP
The horizontal range of the rocket is
Explanation of Solution
Given info: The initial speed of the rocket is
The formula to calculate the displacement of the rocket along the initial line of motion is,
Here,
Substitute
Thus, the displacement of the rocket along the initial line of motion is
The horizontal range of the rocket during constant acceleration is,
Here,
Substitute
The horizontal range of the rocket during free fall is calculated as,
Here,
Substitute
The total horizontal range of the rocket is,
Substitute
Conclusion:
Therefore, the horizontal range of the rocket is
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