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 41.0 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
m/s

(b) the direction of the vehicle's velocity relative to the space station Express the direction as an angle measured from the +y direction.
° to the right of the +y direction

Explanation / Answer

To do this you need the basic kinematic equations and a coordinate system. To make things easier pick a coordinate system where the space station is at the origin the x+ direction is to the right... Then remember you can express the rockets velocity and acceleration in component form. The basic equations you'll want to use are Vx= V0x + ax*t, where Vx is the velocity in the x direction, Vo is the initial velocity in the x direction, ax is the acceleration in the x direction, and t is time. This equation also works for the y component just change the subscripts. Once you've calculate the velocity components you can find the magnitude. Remember that velocity is a vector, to find a vector's magnitude you use the Pythagorean Theorem that is |V|^2= (Vx^2+Vy^2). To find the direction of the velocity, you'll need some basic trig. If you draw the velocity vector, it will make a right triangle with its x and y components where the magnitude of the velocity is the length of the hypotenuse, and the value of the components are the lengths of their respective sizes. Since you want the angle to right of the y-axis, call it phi, you'll need to use one of the basic trig functions Sin, Cos, or Tan. Say you pick Tan, remember that Tan is equal to the length of the opposite side over the adjacent side, in this case Tan(phi)= Vx/Vy. Taking the inverse tangent will give you the angle.

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