A rocket travels vertically away from the surface of Mars. It is still close to the surface and travelling at a speed of 25 m s when it jettisons an empty fuel tank. The fuel tank initially travels with the velocity of the rocket, but it is attracted to Mars and reaches the surface, where it impacts at a speed of 75 m s. Calculate the time interval between the fuel tank braking loose and impacting the surface of Mars, assuming that the magnitude of the acceleration due to gravity near Mars’s surface is 3.7 m s.

Question

A rocket travels vertically away from the surface of Mars.  It is still close to the surface and travelling at a speed of 25 m s when it jettisons an empty fuel tank.  The fuel tank initially travels with the velocity of the rocket, but it is attracted to Mars and reaches the surface, where it impacts at a speed of 75 m s.  Calculate the time interval between the fuel tank braking loose and impacting the surface of Mars, assuming that the magnitude of the acceleration due to gravity near Mars’s surface is 3.7 m s.

v=u+at
where I am looking for t. 
So 
75=25+3.7t
t=13.5s
But I know the answer is 27s so somewhere I need to multiply t by 2 but im not sure how this is achieved from v=u+at? do I need to find the displacement first?

Steve · Answer

The initial 25 m/s is upward The acceleration is downward: -3.7 m/s^2 The final impact speed is also downward. 25 - 3.7t = -75 3.7t = 100 t = 27.03 seconds

Anon · Answer

Great steve thank you! knew it was simple.