# [SOLVED] Rocket Acceleration?

by ae4jm
Tags: acceleration, rocket, solved
 P: 79 1. The problem statement, all variables and given/known data 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 6 seconds later. What was the rocket's acceleration? 2. Relevant equations Vf=Vi + at y=Vi(t)+.5a(t^2) Vf^2=Vi^2+2(a)(y) 3. The attempt at a solution First problem of this type that I've seen in our homework questions. I'm wandering with what information I should begin with first. I know there is constant acceleration, the bolt falls off the rocket at t=4s after launch, and that t=6s the bolt hits the ground. What should I already notice about this problem? I know that there is something that I'm overlooking.
 Sci Advisor HW Helper P: 4,301 Try working backwards. You know how long it takes the bolt to fall. Then you can calculate its initial altitude. Obviously, that is the "final" altitude of the rocket, whose initial altitude is zero. Then try to get the acceleration of the rocket.
 P: 79 I'm sorry, I'm still lost. Wouldn't I have to know the velocity or acceleration to find the altitude?
Mentor
P: 14,243

## [SOLVED] Rocket Acceleration?

You don't know the rocket's acceleration, so use a symbol for that -- call it $a$. Express the position and velocity of the rocket as a function of time $t$ and this unknown acceleration $a$. You know the exact time at which the bolt shakes loose. What are the position and velocity of the bolt at this time?

The bolt accelerates downward due to gravity after shaking loose. What is the general expression for the height of a falling object given an initial height and velocity? You know the initial height and velocity as a function of $a$ and you know the time at which the height becomes zero. Solve for $a$.
 Emeritus Sci Advisor PF Gold P: 5,540 1.) Write down a function for the y-coordinate $y(t)$ of the bolt as a function of time in the interval $0\leq t\leq4$. Since it's traveling with the rocket, the function will be in terms of the acceleration $a$. Using this function, determine the position and velocity of the bolt at $t=4$. 2.) Write down a function for the y-coordinate of the bolt as a function of time in the interval $4\leq t\leq6$. Remember that now the bolt is in freefall, so what is its acceleration here? Use the fact that the position and velocity functions are continuous. 3.) You know that $y(6)=0$. Use that fact to obtain the acceleration $a$ of the rocket.