Projectile Problem: Solving an Artillery Shell Problem

[Zdub311]

Homework Statement

An artillery shell is fired from the origin in the x direction(z is vertically upward) at an angle of 30degrees above the horizontal axis at a velocity of 3000 ft/s. after 2.5a the shell which weighs 100lb explodes into two pieces. The first piece to land weighs 30 lbs and lands at (900,400,0)ft at 4.5 s after the gun was fired. When and where does the other piece land? Neglect air resistance and assume

Homework Equations

Not sure on these but I have x_e=v cos theta(t) and z_e=v sin theta(t)_e -1/2gt_e^2 and t_e=o

The Attempt at a Solution

Really need some inspiration with this one guys. This is my first physics class btw!

Thank you for any attempted help.

 

[Zdub311]

Although a 3000 level undergrad physics course. This question probably belongs in the beginner forum!

 

[nejibanana]

I would use the kinematic equations, I think they are what you have listed, the notation throws me off a bit. Using those you should be able to find the velocity of the particle at the point it explodes, and also find out the velocity and angle of the first piece. From there conservation of momentum should be able to give you the velocity and angle for the second piece, and using the kinematic equations once again will give you what it asks for. This assumes the explosion doesn't impart any energy into the pieces.

 

[AlephZero]

This assumes the explosion doesn't impart any energy into the pieces.

A change in kinetic energy doesn't matter. The assumption is that the two pieces contain all the mass of the shell. That means you can use conservation of momentum at the time when the shell explodes.

Find where the shell is at 2.5s.
Then find the velocity vector after the explosion for the 30lb piece, so it lands at the given time and place.
Then use conservation of momentum to find the velocity vector of the other piece after the explosion.