Aspace vehicle is coasting at a constant velocity of 21.4 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 0.301 m/s2 in the +x direction. after 38.9 s, the pilot shuts off the rcs thruster. after the rcs 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 (in degrees) measured from the +y direction.

a) S = 24.4 m/s

b) angle from the +y direction = 28.7°

Explanation:

1) Data

Vy = 21.4 m/s = constant

Vy,o = 0

Ax = 0.301 m/s²

t = 38.9 s

a) V = ?

b) angle=?

2) Formulas

i) Vy = constant = Vy,o

ii) Vx = Vx,o + Ax t = 0 + Ax t = Ax t

3) Solutions

a) speed

t = 38.9 s and Vx,o = 0.301 m/s² ⇒ Vx = 0.301 m/s² × 38.9s = 11.7 m/s

V² = Vx² + Vy² = (11.7 m/s)² + (21.4m/s)² = 594.85 m² / s²

⇒ V = 24.39 m/s

b) angle measured from the +y direction

tan (angle) = Vx/Vy = 11.7 m/s / 21.4 m/s = 0.5467

angle = arctan(0.5467) ≈ 28.7°

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