It is 2058 and you are taking your grandchildren to Mars. At an elevation of 58.

Question

It is 2058 and you are taking your grandchildren to Mars. At an elevation of 58.9 km above the surface of Mars, your spacecraft is dropping vertically at a speed of 363 m/s. The spacecraft is to make a soft landing -- that is, at the instant it reaches the surface of Mars, its velocity is zero. Assume the spacecraft undergoes constant acceleration from the elevation of 58.9 km until it reaches the surface of Mars. How much time will it take the spacecraft to reach the surface of Mars from the elevation of 58.9 km? please show work

Explanation / Answer

initial velocity u = 363 m/s

h = 58.9 Km = 58900 m

final velocity v = 0

let the acceleration be a

using third equation of motion we get

v2 = u2 + 2ah

0 = 3632 + 2 a(58900)

- 1.32 X 105 = 2a(58900)

a= - 1.32 X 105 /(2 X 58900)

a = -1.12 m/s2

using first equation we have

v = u + at

0 = 363 + (-1.12)t

1.12t = 363

t = 324.1 s

t = 5.4 mins

time taken by spacecraft to reach surface of mars is 5.4 mins

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