A space vehicle is coasting at a constant velocity of 21.0 m/s in the + y direct

Question

A space vehicle is coasting at a constant velocity of 21.0 m/s in the + y direction relative to a space station. The pilot of the vehicle fires a thruster, which causes the vehicle to accelerate at 0.320 m/s2 in the + x direction. After 45.0 s, the pilot shuts off the thruster. After the thruster is turned off, find (a) the magnitude and (b) the direction of the vehicle's velocity relative to the space station. Express the direction as an angle measured from the + y direction.

When I went through this problem. I got a magnitude of 35.4 and an angle of 59.3. Something went wrong and I am not sure where. Please help.

Explanation / Answer

The initial velocity in the x direction is zero; after 45 sec acceleration of .320m/s^2 in x direction, the velocity is 14.4 m/s. The y velocity of 21 m/s is unchanged, as there was no y acceleration.

The magnitude of the velocity is sqrt(14.4^2 + 21^2) = 25.5 m/s

The angle measured from the +y direction is tan^-1(14.4/21)= 34.4 degrees clockwise from +y.

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