What is the rockets momentum after the course change?

[sidge2222]

Homework Statement

A rockets course needs to be diverted by one degree. The mass of the rocket is 2000kg, and its forward velocity is 15000ms. The rocket has side rockets with a thrust of 25000N with which to effect course change.

a) What is the rockets momentum after the course change?
b) How long must a side rocket fire to effect the required course change?

Homework Equations

momentum = mv
f = change in mv/t
tan angle = sum of i/sum of j

The Attempt at a Solution

if momentum = mv, then 2000 x 15000 = 30,000,000.
im pretty sure the answer is not as simple as this due to the change in the angle, but I am thinking the change in the angle won't effect the momentum of the rocket because the velocity and mass remain the same.

Am i missing something here guys or is it really that simple?

Thanks for reading, Sidge

 

[gneill]

if momentum = mv, then 2000 x 15000 = 30,000,000.
im pretty sure the answer is not as simple as this due to the change in the angle, but I am thinking the change in the angle won't effect the momentum of the rocket because the velocity and mass remain the same.

Am i missing something here guys or is it really that simple?

Thanks for reading, Sidge

Momentum is a vector quantity. A change in direction counts, even if the speed of the rocket doesn't change. So there's a $$\Delta$$p that was accomplished by expending fuel. That's going to reduce the mass of the rocket accordingly, and change the magnitude of the momentum.

 

[sidge2222]

Thanks for the response gneill.

Ok, so if i need calculate a change in angle by one degree, i would use the equation of tan angle = sum of i/sum of j, and then arrange these values until i alter the angle by one degree.

That sound right guys?

Thanks, Sidge

 

[gneill]

Thanks for the response gneill.

Ok, so if i need calculate a change in angle by one degree, i would use the equation of tan angle = sum of i/sum of j, and then arrange these values until i alter the angle by one degree.

That sound right guys?

Thanks, Sidge

Consider that the problem statement doesn't explain *how* the 25000N thrust is created. In the real world, this would be by throwing out fuel mass at some high velocity (a rocket engine). This changes the mass of fuel on board the ship at it fires, etc., with all the subsequent details.

But here there are no details about the thrusters other than the force they can apply. So why not assume that they are "magic" and don't consume any ship's mass?

Now consider what happens when you apply a constant thrust at right angles to the instantaneous velocity. What shape trajectory happens?

 

[rwisz]

Your solution is correct. The change in angle will not affect the momentum of the rocket, as long as the mass and velocity remain constant. The momentum of the rocket after the course change will still be 30,000,000 kgm/s.

To calculate the time it takes for the side rockets to effect the required course change, we can use the equation f = change in mv/t. In this case, the force (f) is the thrust of the side rockets, which is 25000N. The change in momentum (change in mv) is the difference between the initial momentum (30,000,000 kgm/s) and the final momentum (30,000,000 kgm/s). So the equation becomes:

25000N = (30,000,000 kgm/s - 30,000,000 kgm/s)/t

Solving for t, we get t = 0. So the side rockets must fire for 0 seconds to effect the required course change. This may seem counterintuitive, but it makes sense because the momentum of the rocket remains constant, so there is no change in momentum to be achieved by the side rockets.

I hope this helps clarify your understanding of the problem. Keep up the good work in your studies!