A space vehicle is coasting at a constant velocity of 20.6 m/s in the +y directi

Question

A space vehicle is coasting at a constant velocity of 20.6 m/s in the +y direction relative to a space station. The pilot of the vehicle fires a RCS (reaction control system) thruster, which causes it to accelerate at 0.290 m/s2 in the +x direction. After 49.0 s, the pilot shuts off the RCS thruster. After the RCS thruster is turned off, find the following quantities.


(a) the magnitude of the vehicle's velocity

(b) the direction of the vehicle's velocity relative to the space station Express the direction as an angle measured from the +y direction. <---- Should be a degree

Explanation / Answer

The velocity in the positive x direction, at the end of the acceleration = 0.29 m/s^2 * 49 s = 14.21 m/s

The magnitude of the velocity = x velocity^2 + y velocity^2)^0.5
(20.6^2 + 14.21^2)^0.5 = 25.03 m/s

The tangent of the angle to the right of the +y direction = (x velocity ÷ y velocity. This angle is clockwise from the +y axis.

Tan = 25.03/14.21 = 1.76
= tan^-1 (1.76)

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