Magnitude of Initial velocity of Spacecraft

[dragon18]

On a spacecraft two engines fire for a time of 572 s. One gives the craft an acceleration in the x direction of ax = 5.15 m/s2, while the other produces an acceleration in the y direction of ay = 7.41 m/s2. At the end of the firing period, the craft has velocity components of vx = 3782 m/s and vy = 4842 m/s. Calculate the magnitude of the initial velocity.


I'm not sure what equations to use.



Attempt
add the square root of 3782 and the square root of 4842
take the square root of the sum 131.082
=11.42 m/s(incorrect)

 

[Simon Bridge]

I'm not sure what equations to use.

This is motion with constant acceleration isn't it?
Use the suvat equations.

Attempt
add the square root of 3782 and the square root of 4842
take the square root of the sum 131.082

You are saying you did: $\sqrt{\sqrt{v_x}+\sqrt{x_y}}$ ?

=11.42 m/s(incorrect)

Well yes - it would be.

1. those numbers are the final velocities
2. the magnitude of a vector is $|\vec{v}|=\sqrt{v_x^2+v_y^2}$

 

[dragon18]

so do I use the equation v=u+at?

 

[Simon Bridge]

Try it and see.

 

[dragon18]

which number do I use though? It keeps telling me its wrong no matter what I put

 

[Simon Bridge]

Please show your working.