A spacecraft on its way to Mars has small rocket engines mounted on its hull; on

Question

A spacecraft on its way to Mars has small rocket engines mounted on its hull; one on its left surface and one on its back surface. At a certain time, both engines turn on. The one on the left gives the spacecraft an acceleration component in the x direction of ax = 5.10 m/s2, while the one on the back gives an acceleration component in the ydirection of ay = 7.30 m/s2. The engines turn off after firing for 675 s, at which point the spacecraft has velocity components of vx = 3630 m/s and vy = 4276 m/s.

What was the magnitude and direction of the spacecraft's initial velocity, before the engines were turned on?

Express the direction as an angle measured counterclockwise from the +x axis.

Explanation / Answer

v0x = vx - ax t = 3630 - (5.10) * (675) = 187.5 m/s

v0y = vy - ay t = 4276 - (7.30) * (675) = -651.5 m/s

Magnitude:

v = sqrt((187.5)y2 + (-651.5)y2) = 678 m/s

direction:

theta = 360 - tan-1(651.5/187.5) = 286 degrees

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