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.

|Fh|,|Fv|=

Explanation / Answer

Here ,

initial horizontal speed, vx = 33 m/s

height , h = 1200 m

time of free fall , t = 20 s

a)

speed after 20 s

vy = g * t = 3.7 * 20

vy = 74 m/s

height at 20 s

h = 1200 - 0.5 * 3.7 * 20^2

h = 460 m

time taken to stop ,

v^2 - u^2 = 2 a* d

74^2 = 2 * 460 * a

a = 5.95 m/s^2

Now , time taken to stop ,

0 = 74 + 5.95 * t

t = 12.43 s

Now , Fh = (33/12.43) * 150

Fh = 398 N

NOw , Fv - 150 * 3.7 = (74/12.43) * 150

Fv = 1448 N

the horizontal component of the force is 398 N , vertical force is 1448 N

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