A space vehicle is coasting at a constant velocity of 20.8 m/sin the +y directio

Question

A space vehicle is coasting at a constant velocity of 20.8 m/sin the +y direction relative to a space station. Thepilot of the vehicle fires a RCS (reaction control system)thruster, which causes it to accelerate at 0.270 m/s in the +xdirection. After 43.0s, the pilot shuts off the RCSthruster. After the RCS thruster is turned off, find thefollowing quantities. (a) the magnitude of the vehicle's velocity. ____ m/s (b) the direction of the vehicle's velocity relative to thespace station. Express the direction as an angle measuredfrom the +y direction. _____degrees to the right of the +ydirection. A space vehicle is coasting at a constant velocity of 20.8 m/sin the +y direction relative to a space station. Thepilot of the vehicle fires a RCS (reaction control system)thruster, which causes it to accelerate at 0.270 m/s in the +xdirection. After 43.0s, the pilot shuts off the RCSthruster. After the RCS thruster is turned off, find thefollowing quantities. (a) the magnitude of the vehicle's velocity. ____ m/s (b) the direction of the vehicle's velocity relative to thespace station. Express the direction as an angle measuredfrom the +y direction. _____degrees to the right of the +ydirection.

Explanation / Answer

   initial velocity in horizontal direction, Ux= 0 m/s    initial velocity in vertical direction, Uy =20.8 m/s    acceleration in +ve x-direction, a = 0.27m/s^2    Final velocity in x direction, Vx = Ux + a t= 0 + 0.27 * 43 = 11.61 m/s    Final velocity in y direction, Vy = Uy =20.8 m/s (a)    magnitude of vehicle's velocity, V = [(Vx)2 + ( Vy )2 ] 1/2 =23.82 m/s (b)    direction of velocity, = arc tan (Vx / Vy ) = arc tan ( 11.61 / 20.8 ) = 26.17o ( to the right ofy-direction )

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