A space probe is descending towards the surface of Mars. When it is at a height

Question

A space probe is descending towards the surface of Mars. When it is at a height of H meters above the surface, it has a speed of 5m/s. At this height, a robot vehicle will be released which will free fall to the surface. g on Mars is 4 m/s^2, and the resistance offered by the Martian atmosphere can be neglected. The robot vehicle is protected at impact by inflated balloons, but you know that it will be damaged if it hits the surface traveling at a speed greater than 30 m/s. What is the maximum time in seconds for which the robot vehicle could be in free fall without sustaining damage? What is the time interval between release of the vehicle and impact with the surface if released at a height of 50 meters?

Explanation / Answer

When a space probe is at a height of 'H' above the surface of Mars, it has initial velocity of 5 m/s where g on Mars is 4 m/s2.

a) when it reached to the surface of maximum 30 m/s, it will not be damaged. So

maximum Time to reach safely to the surface is found as t by applying formula:

v = u+gt

Hence t will be v - u/(g)

t = (v-u)/g = (30-5)/4 = 25/4 = 6.25 s

b) when the vhicle is free fall to the surface at a height of 50 m, time interval between release of vehicle and impact with the surface will be found by

(2H/g)1/2 = (2*50/4)1/2 = 5 s

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