Rocket Acceleration: Finding the Unknowns with Known Time and Distance

In summary, the rocket's acceleration is constant and it takes 2/3 the time to travel with the ship than only with gravity affecting it.
  • #1
frostking
21
0

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!
 
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  • #2
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.
 
  • #3
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 accleration 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.
 
  • #4
frostking said:
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:)
 

FAQ: Rocket Acceleration: Finding the Unknowns with Known Time and Distance

What is rocket acceleration?

Rocket acceleration refers to the rate at which a rocket's velocity changes over time. It is measured in meters per second squared (m/s^2) and is influenced by factors such as the rocket's thrust, mass, and air resistance.

How is rocket acceleration calculated?

Rocket acceleration can be calculated using the equation a = F / m, where a is the acceleration, F is the force exerted by the rocket's engines, and m is the mass of the rocket. This equation is based on Newton's second law of motion.

What factors affect rocket acceleration?

Several factors can affect rocket acceleration, including the rocket's thrust, mass, and air resistance. The amount of thrust produced by the rocket's engines determines the force pushing it forward, while the rocket's mass affects its inertia and how easily it can be accelerated. Air resistance, or drag, also plays a role in the rocket's acceleration as it moves through the atmosphere.

How does rocket acceleration change over time?

Rocket acceleration typically increases over time as the rocket's engines continue to produce thrust. However, as the rocket travels higher into the atmosphere, air resistance may also increase, causing the acceleration to decrease. Eventually, the rocket will reach a point of maximum acceleration and then begin to slow down as it approaches its maximum velocity.

How does rocket acceleration differ from rocket velocity?

Rocket acceleration and velocity are related but distinct concepts. Acceleration refers to the rate of change of velocity over time, while velocity is the speed and direction at which the rocket is traveling at any given moment. A rocket can have a constant acceleration while its velocity changes, and vice versa.

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