Calculate Rocket Fuel Mass for Course Change | 4350 kg Rocket in Space

[whereisccguys]

A 4350 kg rocket is traveling in outer space with a velocity of 126 m/s toward the Sun. It needs to alter its course by 24.8°, which can be done by shooting its rockets briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 2240 m/s relative to the rocket, what mass of gas must be expelled? Your answer must be accurate to within 1%.

um... i have like no clue how to start on this... anyone give me a start?

 

[scholzie]

Split your 24.8 degree angle into components. Realize that the rocket has an initial momentum in the x direction, and by firing rockets all in the y direction, it will move up, adding a y-component to the final velocity vector.

You will need to use conservation of momentum with vectors, where the rocket initially has no momentum in the y, and the gasses add a momentum of mv...v is known, you need m.

You will have to use a rocket thrust equation, since the mass of the rocket is changing as it's ejecting fuel.
$$\int_{v_1}^{v_2}{dv}=\int_{M_1}^{M_2}\frac{1}{M}{dM}$$

 

[Janitor]

Just to get you started, note that the speed that the firing of the rocket needs to achieve in the perpendicular direction is such as to make the ratio of that speed to 126 m/s be equal to the tangent of 24.8 degrees.

Note also that 126 m/s is not very fast--airplanes can fly faster than that. So my intuition says that the propellant consumption for this event will be small compared to the 4350 kg of initial mass, such that you may not need to take the changing mass of the rocket into account to get within 1% of the right answer.

 

[scholzie]

Not you may not need to take the changing mass of the rocket into account to get within 1% of the right answer.

Good point. Time will tell :)

 

[Janitor]

Scholzie got there first.

A more careful answer would involve taking the changing rocket mass into account, as he points out.