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, component in the y direction of ay -7.30 m/s. The engines turn off after firing for 640 s, at which point the spacecraft has velocity components of while the one on the back gives an acceleration 3545 m/s and vy 4012 m/s. What was the magnitude and the direction of the spacecraft's initial velocity before the engines were turned on? Express the magnitude as m/s and the direction as an angle measured counterclockwise from the +x axis. magnitude direction m/s counterclockwise from the +x-axis

Explanation / Answer

initial velocity V= (vx^2+vy^2)^1/2

where vx +5.10*640 = 3545 . so, vx = 281m/s

and vy +7.30*640 = 4012 . so, vy = -660m/s

so, V = (281^2+660^2)^1/2 = 717.3m/s

and along tan^-1(281/-660) = 337 degrees counterclockwise from the +x axis

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