Kinematics problem- seems easy but having trouble

[G01]

So the problem is this: A rocket is launched straight up with a constant acceleration. Four seconds after liftoff a bolt falls off the rocket and hits the ground 6 seconds later. What was the rockets acceleration?

Well the initial velocity of the rocket is 0m/s and the velocity of the rocket at four seconds is equal to the initial velocity of the screw. The acceleration of the screw is -g and at first I assumed the distance the bolt fell is the same as the distance the rocket went up but i didn't take into account the fact the the bolt would continue to move up for a tiny bit before it started to fall. Thats all I can get , can someone point me in the right direction here. I know I know how to solve it but i can't find a formula or group of formulas to use.

Thanks a lot

 

[JoAuSc]

The 1D kinematic equations for a constant acceleration is:

x(t) = x_o + v_o*t + at^2/2, v(t) = dx/dt = v_o + at

Let r(t) = the position of the rocket, and s(t') = the position of the screw, where t' = t-4. It's easy to find the kinematic equation for the rocket. As for the screw, its initial position is r(4) and its initial velocity is v_r(4), where v_r(t) is the velocity of the rocket. Obviously, the acceleration of the screw is zero. Figure out what s(t'=6) is and solve for a.

 

[DaMastaofFisix]

Just for kicks, how did you come up with the notion that the acceleration of the screw is zero? I am 100 percent sure that there is not only no need for calculus, but that the acceleration is never zero. Unless I too skipped something in this problem, I found the soltion wih just some simple algebraic substitution. If you both are interested, let me know.

 

[JoAuSc]

Just for kicks, how did you come up with the notion that the acceleration of the screw is zero? I am 100 percent sure that there is not only no need for calculus, but that the acceleration is never zero. Unless I too skipped something in this problem, I found the soltion wih just some simple algebraic substitution. If you both are interested, let me know.

Nope, you're right, the acceleration of the screw is never zero. What I meant to say is that the contribution to the acceleration by the rocket for the screw is zero for any time after four seconds.