Solve Projectile Fragments Problem with Hint

[heartofaragorn]

Homework Statement

A fireworks rocket is fired with a speed of 80 m/s at an angle of 60 degrees above the horizontal. At the highest point of its trajectory, the projectile explodes into two fragments, one three times heavier than the other. The two fragments hit the ground at the same time, and the heavier fragment is hurled backwards so it lands at the same point from which it was launched.

How far away from the launch point does the lighter fragment land? How much energy was converted from chemical energy during the explosion into kinetic energy?

Homework Equations

Not a clue

The Attempt at a Solution

Looked through my professor's lecture notes and example problems, looked through the applicable chapters in the book...and I can't seem to find any problem that resembles this one. I'm completely and utterly stumped. If someone could just give me a hint as to the appropriate equations, I think I can figure it out...but I just have no clue.

 

[chaoseverlasting]

You're supposed to use the conservation of linear momentum. At the highest point, the particle is in horizontal equilibrium, hence, m1(v1)=-m2(v2). Since m1=3m2, v2=3v1 (in opposite direction).

Using this, you should be able to solve for v1, and hence v2. From there you can find the kinetic energy.

 

[heartofaragorn]

Ohhhh. I don't think I've ever seen those formulas. Thank you!

 

[chaoseverlasting]

Then you better look up conservation of linear momentum.