Inelastic Collision and Finding Initial Velocity

[pitaaa]

Collisions and Determining the Original Speed

Homework Statement

Two spacecraft s from different nations have linked in space and are coasting with their engines off, heading directly toward Mars. The spacecraft s are thrust apart by the use of large springs. Spacecraft 1, of mass 1.9 x 10^4 kg, then has a velocity of 3.5 x 10^3 km/h at 5.1 degrees to its original direction, and spacecraft 2, of mass 1.7 x 10^4 kg, has a velocity of 3.4 x 10^3 km/h at 5.9 degrees to its original direction. Determine the original speed of the spacecraft s when they were linked together.

Homework Equations

mv₁ + mv₂ = mv₁' + mv₂'
p = mv

The Attempt at a Solution

Since there are angles, I tried looking for the components. So, the components of the 3.4 x 10^3, are x= 3.4x10^3cos5.9 and y=3.4x10^3sin5.9. The components of the 3.5 x 10^3 km/h are x= 3.5x10^3cos5.1 and y=3.5x10^3sin5.1. I'm having a difficult time understanding what to do from here. So we're given the final velocities of both, and their angles. How do I incorporate the components? Where do I sub them in? So, both must have the same initial velocity, so you can simplify the equation slightly:

since v1=v2
v(m₁ + m₂) = mv₁' + mv₂'

If anyone could give me a hint, that'd be GREAT =)

 

[aniketp]

Momentum is conserved along the direction perpendicular to the initial motion.
Also since the andle of divergence is given you could add them vectorially...

 

[redmafiya]

Suppose their common speed before separation is v,
Spacecraft 1's speed after separation is v₁
Spacecraft 2's speed after separation is v₂

Note that in this case, the momentum is conservative along both the x and y directions.
So
Along X axis: (m₁ + m₂)v = m₁v₁cos(5.1⁰) + m₂v₂cos(5.9⁰)
Along Y axis: 0 = m₁v₁sin(5.1⁰) - m₂v₂sin(5.9⁰)

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