Physics problem...

[RoyalXBlood]

I really would like to figure out how to do this, it's the only problem I can't solve so far..

 

"A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 7.00 later."

 

"What was the rocket's acceleration?"

 

We are focusing on three equations:

1) v = v(initial) + at

2) (delta)x = vt + .5at^2

3) v^2 = v(initial)^2 + 2a(delta)x

 

x = distance

v = velocity

a = acceleration

t = time

(delta)x = x(final) - x(initial)

[Bignose]

Firstly, because this is the homework forum, we will help you discover the answer on your own, not do the work for you.

 

I have some questions I think will help guide you to solving the problem.

 

1) What are the forces on the rocket?

 

2) At the moment the bolt falls off the rocket, what are the forces on it?

 

3) What would be initial conditions of the bolt when it falls off the rocket?

 

Just as a final hint, this will require the solution of two unknowns using two equations.

 

Fortunately, you have two objects about which to write two equations.

 

Answer those above questions, and write down what two equations you think will help you, and if you are still stuck, I'll try to come back and help further. Or someone else will probably come along and help, further, too.

[RoyalXBlood]

1) What are the forces on the rocket?

It has a constant positive acceleration.

 

2) At the moment the bolt falls off the rocket, what are the forces on it?

It will start to deaccelerate due to gravity.

 

3) What would be initial conditions of the bolt when it falls off the rocket?

The initial velocity would be equal to the velocity of the rocket at the moment it fell off.

 

So I know V(inital of bolt) = V(final of rocket)

I know I can use V(final of rocket)=4a, which means the inital velocity of the bolt with be 4a. But I dont know where to go with that.

 

And I know the bolt will continue to go up and velocity will eventually be 0 and then come back down. I know it's acceleration is -9.8m/s^2, but I don't know if that matters.

[Bignose]

Ok, so do the last part of my recommendation.

 

I find that when you are stuck on something like this. You want to write out in math every equation that you think may be applicable, and identify the knowns and the unknowns.

 

So, write out the equations that apply, and identify what you do know, what can be figured out, and what cannot be figured out.

[swansont]

And I know the bolt will continue to go up and velocity will eventually be 0 and then come back down. I know it's acceleration is -9.8m/s^2, but I don't know if that matters.

 

Yes, it matters.

 

Equation 1 gives you the speed of the rocket (and bolt) at the 4-second mark, as you've already suggested.

 

We don't know how high the rocket went, but we know that however high it went is also the distance the bolt has to fall. Try writing down equation 2 for the rocket and for the bolt. Since delta-x is the same, you can set them equal to each other.

[RoyalXBlood]

I guess I didn't really think about that because I was thinking about the distance the bolt would fly up and then down. The distance would be greater than what the rocket traveled but the formula only cares about displacement. And since the rocket went up and the bolt is going down I would slap a negative on one side to correctly evaluate it right?

 

So would this be the right set up?

 

-[0(4) + (1/2)a(4)^2] = 4a(7) + (1/2)(-9.8)(7)^2

 

If so, after a little algebra I get a=6.67m/s^2

Edited September 23, 2008 by RoyalXBlood
typo