Splitting Comet Momentum Problem Solutions

[kariibex]

Homework Statement

A comet of mass 6000 kg traveling at 30 000 m/s splits into two pieces that move apart with velocities that make equal angles of 20° relative to the original trajectory. If one piece is found to be 5 times the mass of the other...calculate the mass of each piece, find the impulse of the system, and calculate the velocities of the two pieces.

Homework Equations

P = mv
P total before = P total after
Impulse = ΔP

The Attempt at a Solution

Mass 1 = 1000 kg and Mass 2 = 5000kg

i assumed that mass one traveled 20° above the horizontal, while mass two traveled 20° below the horizontal.

So;

P before = mv = (6000kg)(30 000 m/s) = 1.8 x 10^8 kg m/s [+x]

P1 after = m1v1 = 1000v1 kg m/s [+x 20° +y]
P1 after X = 1000(v1) kg m/s cos20° = 939.69(v1) [+x]
P1 after Y = 1000(v1) kg m/s sin20° = 342.02(v1) [+y]

P2 after = m2v2 = 5000v2 kg m/s [+x 20° -y]
P2 after x = 5000(v2)cos20° = 4698.46(v2) [+x]
P2 after y = 5000(v2)sin20° = 1710(v2) [-y]

Vector Equations
x: 1.8 x 10^8 kg m/s = 939.69(v1) + 4698.46(v2)
y: 0 = 342.02(v1) - 1710(v2)

I'm not sure how to solve for the velocities at this point, any help is appreciated.
Thank you!

 

[gneill]

Two equations, two unknowns...

 

[kariibex]

Two equations, two unknowns...

I'm allowed to use substitution even though they're in different axis?

 

[gneill]

I'm allowed to use substitution even though they're in different axis?

Yup. V1 and V2 are independent variables that appear in both equations and must have the same values in each!

 

[kariibex]

Yup. V1 and V2 are independent variables that appear in both equations and must have the same values in each!

Ahh! Thank you so much :)