Solve Physics Problem: 3000kg Space Capsule

[bondgirl007]

Homework Statement

A 3000kg space capsule is traveling with a velocity of 200m/s. In an effort to alter its course, it fires a 25.0 kg projecticle perpendicular to its original direction of motion at a speed of 2000 m/s. What is the speed of the capsule and by what angle has its direction changed.

* my teacher said assume mass stays the same*

Homework Equations

P = mv
m1v1 + m2v2 = m1v1' + m2v2'
M = m1 + m2
V = combined velocity

The Attempt at a Solution

MV = m1v1' + m2v2'
(3000)(200) = (3000)(v1') + (25)(2000)
v1' = 1833.3

Is this right so far? I'm very confused and am not sure if I should be using Pythagoras to find it or what?

 

[bondgirl007]

Can anyone please help me out? I've been stuck on this question for over half an hour. :(

 

[Moetasim]

Your solution so far is on the right track. To find the final velocity of the space capsule, you need to use the conservation of momentum equation (m1v1 + m2v2 = m1v1' + m2v2'). However, you also need to take into account the direction of the projectile. Since it is fired perpendicular to the original direction of motion, it will not contribute to the final velocity in that direction. This means that the final velocity of the space capsule in the original direction of motion will be equal to its initial velocity (200 m/s).

To find the final velocity in the direction perpendicular to the original direction of motion, you can use the Pythagorean theorem. The momentum of the projectile in that direction will be equal to its mass (25 kg) multiplied by its final velocity (2000 m/s). This momentum must be equal to the momentum of the space capsule in that direction, which is equal to its mass (3000 kg) multiplied by its final velocity in that direction (v2').

Using these equations, you can solve for v2' and find the final velocity of the space capsule in the direction perpendicular to its original motion. Then, you can use trigonometry to find the angle by which its direction has changed. Remember to use the inverse tangent function to find the angle.

Hope this helps! Keep up the good work.