A space vehicle is coasting at a constant velocity of 21.5 m/s in the + y direct

Question

A space vehicle is coasting at a constant velocity of 21.5 m/s in the +y direction relative to aspace station. The pilot of the vehicle fires a RCS (reactioncontrol system) thruster, which causes it to accelerate at0.310 m/s2 in the +xdirection. After 44.0 s, the pilot shutsoff the RCS thruster. After the RCS thruster is turned off, findthe following quantities. (a) the magnitude of the vehicle's velocity
1 m/s

(b) the direction of the vehicle's velocity relative to the spacestation Express the direction as an angle measured from the+y direction.
2° to the rightof the +y direction (a) the magnitude of the vehicle's velocity
1 m/s

(b) the direction of the vehicle's velocity relative to the spacestation Express the direction as an angle measured from the+y direction.
2° to the rightof the +y direction

Explanation / Answer

    initial velocity in horizontaldirection, Ux = 0 m/s    initial velocity in vertical direction, Uy= 21.5 m/s    acceleration in +ve x-direction, a = 0.31m/s^2    Final velocity in x direction, Vx = Ux + a t= 0 + 0.31 * 44 = 13.64 m/s    Final velocity in y direction, Vy = Uy =21.5 m/s (a)    magnitude of vehicle's velocity, V = [(Vx)2 + ( Vy )2 ] 1/2 =25.46 m/s (b)    direction of velocity, = arc tan (Vx / Vy ) = arc tan ( 13.64 / 21.5 ) = 32.39o ( to the right ofy-direction )    initial velocity in vertical direction, Uy= 21.5 m/s    acceleration in +ve x-direction, a = 0.31m/s^2    Final velocity in x direction, Vx = Ux + a t= 0 + 0.31 * 44 = 13.64 m/s    Final velocity in y direction, Vy = Uy =21.5 m/s (a)    magnitude of vehicle's velocity, V = [(Vx)2 + ( Vy )2 ] 1/2 =25.46 m/s (b)    direction of velocity, = arc tan (Vx / Vy ) = arc tan ( 13.64 / 21.5 ) = 32.39o ( to the right ofy-direction )

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