How do i find the acceleration of the rocket?

Question

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 6.10 s later. Find the acceleration of the rocket. ***I don't want the answer, just how to approach the problem, so far ive been left with two variables (a and t) in one equation***

s=.5at^2 doesnt work because the bolt has the upward initial velocity of the rocket (or so i believe)

Answer 1

The first thing you do, is draw a diagram.

After that, you can see that as soon as the bolt falls off, it stops accelerating up as part of the rocket, and starts accelerating down do to gravity. But it already has some upward velocity that it picked up since the launch.

So you start with the position formula for the bolt,

p = -16 t * t + v t. (Think of throwing a ball off a roof! This is in feet per second)

Then you note that v must be 4a, becasue the bolt accerated for 4 seconds when it was on the rocket. Substitute...

0 = -16 t * t + 4a t

The trick is not to do too much. You don't care how high the rocket was when the bolt fell off.

Good Luck!

Answer 2

Usually for questions like this, one is supposed assume the bolt's initial velocity relative to the thing it hits, i.e. the ground, is zero. If not, there really isn't enough information to determine the bolt's motion up until gravity stops it then pulls it back down. To figure that, you would need to know the rocket's speed at time of separation. Does it mention the rocket's speed or it's rate of acceleration at all? Or, do you have to assume it's a real rocket wanting to achieve escape velocity [even then you would have to be given what orbital level it is trying to attain] and determine its rate of acceleration from launch to T+ four seconds?

Answer 3

The formula for distance traveled under constant acceleration is s=.5*a*t^2. The bolt is in free fall under gravity meaning it accelerates at g = 9.8m/sec^2. From this and the time given you know the altitude of the rocket when the bolt fell. You also know that the rocket traveled 4 seconds to get there. The same formula holds, except this time you know the distance the rocket traveled under acceleration a and the time (4 sec) and you can solve for a.

Answer 4

No, it is not 40 3 m/sec^2. that's by using the fact the one hundred thirty N tension has to conquer the tension of gravity. it extremely is the internet tension that quickens it. So subtract 9.8 m/sec^2 from 40 3, as Steve did.