Answer:
A) <em>328 m</em>
B) <em>80.22 m/s</em>
C) <em>8.18 sec</em>
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Explanation:
A)
Initial acceleration of rocket = 2.25 m/s^2
time before engine failure = 15.4 s
initial velocity u of take off = 0 m/s
distance traveled by the rocket under engine power = ?
we'll use Newton's law of motion in this case
<em>S = ut + </em><em>a</em><em></em>
where S is the distance traveled under rocket's acceleration
S = (0 x 15.4) + (2.25 x )
S = 0 + 266.81 m = <em>266.81 m</em>
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Final velocity under rocket power before failure will be gotten from,
v = u + at
v = 0 + (2.25 x 15.4) = <em>34.65 m/s</em>
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After the engine failure, the rocket decelerates under gravity at the rate of <em>g = -9.81 m/s^s (acts in downwards direction)</em>
The initial velocity upwards under free deceleration is v = <em>34.65 m/s</em>
the final velocity will be at the maximum height where rocket stops i.e
u = 0 m/s
the distance covered in this period of free deceleration will be s = ?
using the equation
= + 2gs
= + 2(-9.81 x s)
0 = 1200.6 - 19.62s
-1200.6 = -19.62s
s = -1200.6/-19.62 = <em>61.19 m</em>
therefore,
Maximum Height = <em>266.81 m</em> + <em>61.19 m = 328 m</em>
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B)
Before descending, at maximum height, the initial velocity of rocket becomes 0 m/s (rocket comes to a stop)
Rocket then descends freely under <em>g = 9.81 m/s^2 (acts in downwards direction)</em>
distance that will be traveled downwards will be <em>328 m</em>
final velocity v before crashing = ?
using = + 2gs
= + 2(9.81 x 328)
= 0 + 6435.36
v = = <em>80.22 m/s</em>
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Time taken to reach the pad will be gotten from
v = u + gt
80.22 = 0 + 9.81t
t = 80.22/9.81 = <em>8.18 sec</em>