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An astronaut is inside a 2.25×106 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 astronauts are in danger of blacking out at an acceleration greater than 4g. What force, in terms of her weight W, does the rocket exert on the astronaut? What is the shortest time it can take the rocket to reach the speed of sound?

Respuesta :

Answer:

a)   F = 88.2 10⁶ N  and b)      t = 8.44 s

Explanation:

With Newton's second law we can work the first part

    F = m a

    a = 4g

    F = 2.25 10⁶ 4 g

    F = 2.25 10⁶ 4 9.8

    F = 88.2 10⁶ N

This is the force that is applied to the rocket, but by action and reaction it is also the force that the rocket applies to all its occupants

To calculate the time we use the kinematic equations, where you assume a constant acceleration produced by the engines

 

      vf = vo + a t

      vf = 0 + a t

      t = vf / a

      t = 331/4 9.8

      t = 8.44 s

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