A space vehicle is coasting at a constant velocity of 17.6 m/s inthe + y directi

Question

A space vehicle is coasting at a constant velocity of 17.6 m/s inthe +y direction relative to a space station. The pilot ofthe vehicle fires a RCS (reaction control system) thruster, whichcauses it to accelerate at 0.218 m/s2 in the +xdirection. After 49.8 s, the pilot shuts off the RCS thruster.After the RCS thruster is turned off, find (a) themagnitude and (b) the direction of the vehicle'svelocity relative to the space station. Express the direction as anangle (in degrees) measured from the +y direction.

Explanation / Answer

therefore vy = +17.6m/s Now initial x - component of velocity is zero. x - component of acceleration is ax =0.218m/s2 then the x - component of velocity of thespace vehicleafter 49.8s is vx = (0.218m/s2)(49.8s)    = 10.8564m/s then the magnitude of velocity of teh space craft is v =[(17.6m/s)2 + (10.8564m/s)2]            = 20.68 m/s
(b)Direction is tan-1(10.8564/17.6) counter clockwise with +x axis       =31.67ocounter clock wise with +x axis then the x - component of velocity of thespace vehicleafter 49.8s is vx = (0.218m/s2)(49.8s)    = 10.8564m/s then the magnitude of velocity of teh space craft is v =[(17.6m/s)2 + (10.8564m/s)2]            = 20.68 m/s
(b)Direction is tan-1(10.8564/17.6) counter clockwise with +x axis       =31.67ocounter clock wise with +x axis

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