You are part of a design team for future exploration of the planet Mars, where g

Question

You are part of a design team for future exploration of the planet Mars, where g= 3.7m/s2. An explorer is to step out of a survey vehicle traveling horizontally at 33 m/s when it is 1200 m above the surface and then fall freely for 20 s. At that time, a portable advanced propulsion system (PAPS) is to exert a constant force that will decrease the explorer's speed to zero at the instant she touches the surface. The total mass (explorer, suit, equipment, and PAPS) is 150 kg. Assume the change in mass of the PAPS to be negligible.

a) Find the horizontal and vertical components of the force the PAPS must exert, and for what interval of time the PAPS must exert it. You can ignore air resistance.

Explanation / Answer

After 20 s, the distance left to fall is 1200 - 1/2 * 3.7 * 20^2 = ? m (call it h).

And at that point, his vertical speed is 3.7 * 20 = ? m/s (call it Vy)

So, in a distance of h he must decrease his vertical speed from Vy to 0 using a constant acceleration (a_y)
a_y = (Vy)^2 / (2h) = ? m/s^2
Multiply that with 150 kg = ? N <=== vertical component

For the time interval:
t = Vy / a_y = ? s

And once you have that, the horizontal acceleration is 33 / t = ? m/s^2
Multiply that with 150 kg = ? N <=== horizontal component

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