Rocket Acceleration: Finding the Unknowns with Known Time and Distance

[frostking]

Homework Statement

A rocket is launched straight up with constant acceleration. Four seconds later a bolt flies off the rocket. The bolt hits the ground 6.0 seconds later. What is the acceleration of the rocket?

Homework Equations

acceleration = change in velocity/change in time
equations involving velocities and distance are of little use since the only knowns are time and that we have constant acceleration.

The Attempt at a Solution

I tired setting up a proportion since it took only 4 seconds for the bolt to travel a set distance on the rocket therefore under the same acceleration and then it took 6 seconds for it to fall to the ground the same distance without the rocket' acceleration. So, it took 2/3 the time to travel with the ship than only with gravity affecting it. However, I can not come up with 5.5 m/second squared which is the correct answer. I am studying for an exam tonight and this simple misconception is really bothersome!

 

[Jack21222]

The reason that doesn't work is the bolt doesn't start at rest when it flies off, it has an initial upward velocity.

Try the kinematic equations, I think you have more than you realize.

 

[MalachiK]

Hi there.

Since all of the accelerations are constant you can use the equations of uniformly accelerated motion. Try writing down two equations for the velocity of the rocket when the bolt falls off in terms of the rocket's acceleration and the time at which the bolt falls off. You can also write down an equation for how high the rocket is (or how far the bolt falls) in terms of the acceleration due to gravity, how long the bolt falls for and the velocity of the rocket when the bolt falls off.

Playing around with these should get you the answer.

 

[davieddy]

equations involving velocities and distance are of little use since the only knowns are time and that we have constant acceleration.

They are all you need!
Let rocket's acceleration be a m/s^2.
What is the speed of the bolt when it "falls off" the rocket?
At what height does this occur?

etc

edit:
MalachiK beat me to it, but great minds think alike:)