How Much Gas Must a Rocket Expel to Alter Its Course by 23 Degrees?

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Homework Statement

A 4200-kg rocket is traveling in outer space with a velocity of 120m/s toward the Sun. It needs to alter its course by 23 degrees, which can be done by shooting is rockets briefly in a direction perpendicular to it’s original motion. If the rocket gases are expelled at a speed of 2200 m/s relative to the rocket, what mass of gas must be expelled?

Homework Equations

momentum = mass x velocity

The Attempt at a Solution

Ok so I'm reviewing for my midterm and I don't remeber how to do this problem

I know I need to calculate the new velocity. That is easy.

Vy = 120 m/s tan 23 = 50.94 m/s

Now supposively the answer is 95 kg.
I can't seem to get this answer for the life of me. I set up a quation like this

m1 V1 = (m1 + mg )Vy

I keep on getting the wrong answer how do i do this. I think i need help setting up the equation becasue I think I'm reading this problem wrong or soemthing here

 

[JaWiB]

Momentum in the "y" direction should be the same before and after. Before, the rocket has no velocity in the y direction, so its momentum in that direction is zero (I suspect you already get this part)

After the rocket burn, you essentially have two objects: the rocket and a mass of gas. Adding the momenta of these in the y direction should give you zero, but keep in mind that the rocket's mass is not the same because it lost some mass of gas. Can you write an equation for this?