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 y direction of

ay = 7.30 m/s2.

The engines turn off after firing for 665 s, at which point the spacecraft has velocity components of

vx = 3695 m/s and vy = 4134 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

Using the equation vx = v0x + axt, we can solve for v0x to get

v0x = vx ? axt = 3585 ? (5.10)(635) = 346.5 m/s

And for the y direction:v0y = vy ? ayt = 4094 ? (7.30)(635) = -541.5 m/s

So the intial velocity is v0 = (346.5, -541.5) m/s. The magnitude is

v0 = sqrt( 346.5^2 + 541.5^2) = 642.87 m/s

The direction is tan?1 (-541.5/346.5) = -57.38 degrees ? below the +x axis

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