A space vehicle is coasting at a constant speed of 21.3 m/s inthe +y direction r

Question

A space vehicle is coasting at a constant speed of 21.3 m/s inthe +y direction relative to a space station. The pilot of thevehicle fires a thruster which causes it to accelerate at 0.35 m/sin the +x direction. After 46.0 seconds the pilot shuts off thethruster. After the thruster is turned off, find: A) The magnitude of the vehicles velocity and B) The direction of the vehicles velocity relative to thespace station. Express the direction as an angle measured from the+y direction. A space vehicle is coasting at a constant speed of 21.3 m/s inthe +y direction relative to a space station. The pilot of thevehicle fires a thruster which causes it to accelerate at 0.35 m/sin the +x direction. After 46.0 seconds the pilot shuts off thethruster. After the thruster is turned off, find: A) The magnitude of the vehicles velocity and B) The direction of the vehicles velocity relative to thespace station. Express the direction as an angle measured from the+y direction.

Explanation / Answer

As there is no acceleration in y direction , So velocity in y direction remains constant = 21.3 m/s Also at end of 46 sec , final velocity in x direction = u+at where u=initial velocity in x direction = 0 a=acceleration = 0.35 m/s2 t= 46 sec So final velocity in x direction = 0.35*46 = 16.1 m/s So total velocity magnitude = (16.12 +21.32 = 26.7 m/s b)angle from y direction = tan-1(Vx/Vy) =tan-1(16.1 / 21.3 ) = 37.1o

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