A manned rocket comes to a halt and then begins to fall towards earth. After som

Question

A manned rocket comes to a halt and then begins to fall towards earth. After some time, at a height of 300m above the surface of the earth, it is falling directly downwards at a velocity of 100m/s. At this point the pilot decides to fire the rocket engines such that he gives himself an upward acceleration of 9.81 m/s^2.

a) Show that he crashes by calculating the stopping distance.
b) Calculate the crash speed.
His co-pilot, in the last moment, advises that perhaps he should either have hit the firing button earlier or else used a different thrust.
c) What should the minimum upward acceleration have been if the crash were to be avoided?
d) How much earlier should he have hit the button?


Please go through the problem step by step with correct value, thanks in advance!

Explanation / Answer

a) Show that he crashes by calculating the stopping distance.

v^2 = 2 a d

100^2 = 2 * 9.81 * d

>>> d = 509.7 m

d = 509.7m is greater that 300 meters, therefore he crashes.

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b) Calculate the crash speed.
His co-pilot, in the last moment, advises that perhaps he should either have hit the firing button earlier or else used a different thrust.

vf^2 - vi^2 = 2 a d

vf^2 - 100^2 = 2 * 9.81 * (-300)

vf = 64.14 64.1 m/s

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c) What should the minimum upward acceleration have been if the crash were to be avoided?

v^2 = 2 a d

100^2 = 2 * a * 300

a = 16.7 m/s2

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d) How much earlier should he have hit the button?

t1 = v1/a1 = (100-64.14)/9.81 = 3.655

t2 = v2/a2 = (100-0)/16.667 = 6.000

t2 - t1 = 6.000 - 3.655 = 2.35 s

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