On a spacecraft two engines fire for a time of 587 s. One gives the craft an acc

Question

On a spacecraft two engines fire for a time of 587 s. One gives the craft an acceleration in the x direction of ax = 5.01 m/s2, while the other produces an acceleration in the y direction of ay = 7.01 m/s2. At the end of the firing period, the craft has velocity components of vx = 3767 m/s and vy = 4809 m/s. Calculate the magnitude of the initial velocity On a spacecraft two engines fire for a time of 587 s. One gives the craft an acceleration in the x direction of ax = 5.01 m/s2, while the other produces an acceleration in the y direction of ay = 7.01 m/s2. At the end of the firing period, the craft has velocity components of vx = 3767 m/s and vy = 4809 m/s. Calculate the magnitude of the initial velocity

Explanation / Answer

Apply the velocity - acceleration formula -

vf - vi = a.t

vfx - vix = ax.t
vfy - viy = ay.t

Now put the values -

vix = vfx - ax.t = 3767 - 5.01×587 = 826.13 m/s

and,
viy = vfy - ay.t = 4809 - 7.01×587 = 694.13 m/s

Therefore, magnitude of vi:
||vi|| = sqrt[(vix)² + (viy²)]
||vi|| = sqrt[(826.13)² + (694.13)²]
||vi|| = 1079.03 m/s

So, magnitude of initial velocity = 1079.03 m/s.

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