Plsssssss help, sorry for the trouble

Question

An unmanned SpaceX rocket is fired off the launchpad in south Texas on a mission to the International Space Station. The rocket travels straight upwards, reaching a constant velocity of 267 m/s, but it explodes into three equal pieces a few seconds later (Elon is distraught). Immediately after the explosion, controllers at NORAD view the first piece moving to the right at 344 m/s, and the second piece moving straight upwards at 204 m/s.

Part A: Draw a picture of the rocket before the explosion and after the explosion. (Hint: your vectors will be momentum vectors!)

Part B: Write an equation(s) using the law of conservation of momentum. (Remember: x and y are two different directions!)

Part C: What is the speed and direction (angle) of the third piece?

Answer 1

The initial vector is 267m (where "m" is the mass of the rocket) with a direction straight up. So, after the explosion the sum of the three pieces must also have a sum of 267m in the y-direction. Since piece "1" moves to the right, it's y-direction component is zero. Piece 2 is moving only in the y-direction but since it's mass is only 1/3m, its momentum vector (in the y-direction) is (204)(1/3)m or 68m. Piece "3" must then have a y-component of 267m - 68m or 199m. Piece 3 had a mass of (1/3m) so:

(1/3m)(v) = 199m or v_3-y = 597 m/s (y-direction component of the velocity of piece 3)

Since there was no x-component of the "before explosion" momentum, then the sum of the x-components after the explosion must be zero. Piece 1 was moving right at 344 but with a mass of 1/3m therefore its momentum (in the x-direction) was (344/3)m. That means piece 3 would have an x-component of (344/3)m to the left. Or the x-component of the velocity of piece 3 is 344 m/s left.

Use the Pythagorean Theorem to calculate the magnitude of the resultant velocity:

magnitude of v₃ = √(597² + 344²) = 689 m/s

Use inverse tangent to calculate the direction. Let θ be the angle above straight left:

θ = tan^-1(597/344) = 60ˆ