Concept explainers
A rocket is launched at an angle of 53.0° above the horizontal with an initial speed of 100. m/s. The rocket moves for 3.00 s along its initial line of motion with an acceleration of 30.0 m/s2. At this time, its engines fail and the rocket proceeds to move as a projectile. Find (a) the maximum altitude reached by the rocket, (b) its total time of flight, and (c) its horizontal range.
(a)
Answer to Problem 39AP
Explanation of Solution
The distance travelled is found from the kinematic equation,
Here,
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The coordinates of the rocket at the end of the powered flight are,
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The speed of the rocket at the end of the powered flight is,
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The components of the initial velocity of the rocket are,
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The rise time during the free fall phase is,
Here,
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The vertical displacement during this time is,
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The maximum altitude reached is,
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Conclusion:
Thus, the maximum altitude reached by the rocket is
(b)
Answer to Problem 39AP
Explanation of Solution
The time taken for the rocket to fall a distance of
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The total time of flight is,
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Conclusion:
The total time of flight is
(c)
Answer to Problem 39AP
Explanation of Solution
The rocket is in free fall for,
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The horizontal displacement during this time is,
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The full horizontal range is,
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Conclusion:
Thus, the horizontal range is
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