An astronaut is inside a 2.25 times 10^6 kg rocket that is blasting off vertical

Question

An astronaut is inside a 2.25 times 10^6 kg rocket that is blasting off vertically from the launch pad. You want this rocket to reach the speed of sound (331 m/s) as quickly as possible, but you also do not want the astronaut to black out. Medical tests have shown that astronauts are in danger of blacking out for an acceleration greater than 4g. What is the maximum thrust the engines of the rocket can have to just barely avoid blackout? Start with a free-body diagram of the rocket. F_thrust = N What force, in terms of her weight W, does the rocket exert on the astronaut? Start with a free-body diagram of the astronaut. F = What is the shortest time it can take the rocket to reach the speed of sound? T = s

Explanation / Answer

a )

the initial velocity of the rocket is u = 0 m/sec

final velocity of the rocket is v = 331 m/sec

and the acceleration of the rocket is 4 g

using equation

Fthrust - m g = m a

Fthrust - m g = m X 4g

Fthrust = 4 mg + mg

Fthrust = 5 m g

Fthrust = 5 X 2.25 X 106 X 9.8

Fthrust = 1.1025 X 108 N

b )

same way like above solved

F - W = M a

F = W + M a

F = W + M X 4g

F = W + 4 Mg

we have W = M g

so F = W + 4 W

F = 5 W

c )

using the kinematic relation

v = u + a t

t = v - u / a

t = 331 - 0 / 4 X 9.8 ( since a = 4g given )

t = 331 / 39.2

t = 8.443877551 sec

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