Free fall acceleration of rocket

In summary, the conversation is about a problem involving a rocket launched with constant acceleration and a bolt falling off the rocket. The person is trying to find the acceleration of the rocket using equations of motion but is getting a different answer than the book. They realize their mistake in taking the initial velocity of the bolt to be zero and are advised to consider the rocket's rise time and displacement of the bolt to find the correct acceleration of the rocket.
  • #1
rich1116
3
0
can someone please help me??

I thought I had the answer to this problem, but it doesn't match the book's answer. I can't figure out what I'm doing wrong. This is the problem:

A rocket is launched straight up with constant acceleration. 4 seconds after liftoff, a bolt falls off the rocket and hits the ground 6 seconds later. What was the rocket's acceleration?

First, I used the free fall acceleration of the bolt, -9.80m/s2 and 6 seconds that if fell for to find its position when it fell off the rocket, which I found to be 176.4m. This would also be the height of the rocket when the bolt fell of. Since the rocket traveled for 4 sec to reach this height, I used this height and time to find the acceleration of the rocket, 22.05m/s2.
The book answer however is 5.5 m/s2.
What am I doing wrong?
 
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  • #2


Hello rich.You took the initial velocity of the bolt to be zero.It is not zero it is the upward velocity that the rocket has at the instant the bolt drops.
 
  • #3


then how do i find the initial velocity?
 
  • #4


You can write it in symbol form.
 
  • #5


i can but symbols won't due me any good. i need a definite numerical answer to the question. i know i can write a bunch of equations but i have no numbers to put into them
 
  • #6


Consider the rocket having risen for 4 seconds
u=0, t=4, a=a(unknown)
you can write v=4a and s=8a(equations of motion)
Now consider the bolt
u=4a, a=9.8,t=6, s=8a(this is the displacement not the distance traveled because the bolt rises a bit before it comes to momentary rest and then falls)
Using the values above write down the equation connecting s,u,a(9.8 and not to be confused with a for the rocket)) and t,plug in the numbers and solve.Make sure you get the minus sign in front of ut ie the displacement and acceleration are down whereas u is up.Good luck with it.
 

1. What is free fall acceleration?

Free fall acceleration is the acceleration that a body experiences when it is falling freely under the influence of gravity. It is a constant value of 9.8 meters per second squared (m/s^2) on Earth, and is represented by the symbol "g".

2. How does free fall acceleration apply to rockets?

Rockets experience free fall acceleration during their initial launch, as they are propelled upwards by the force of their engines. Once the engines shut off, the rocket will continue to accelerate due to the force of gravity until it reaches its maximum height and begins to fall back to Earth.

3. What factors affect the free fall acceleration of a rocket?

The free fall acceleration of a rocket is affected by the mass of the rocket, the force of its engines, and the gravitational pull of the planet it is launching from. Other factors such as air resistance and wind can also affect the acceleration.

4. How is free fall acceleration of a rocket measured?

The free fall acceleration of a rocket can be measured using a variety of methods, including using accelerometers or by analyzing data from the rocket's flight path. Additionally, mathematical equations such as Newton's second law of motion can be used to calculate the acceleration.

5. Can the free fall acceleration of a rocket be changed?

Yes, the free fall acceleration of a rocket can be changed by adjusting the force of its engines or the mass of the rocket. For example, increasing the force of the engines will result in a greater free fall acceleration, while adding more weight to the rocket will decrease the acceleration.

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