Solving the Velocity and Displacement of a Package After an Explosion

[Clutch306]

Just need some help getting started. What is it i need to use to get (a)

A suspicious package is sliding on a frictionless surface when it explodes into three pieces of equal masses and with the velocities:
(1) 7.0 m/s, north;
(2) 4.0 m/s 30 degrees south of west;
(3) 4.0 m/s 30 degrees south of east.

(a)What is the velocity(both magnitude & direction) of the package before it explodes?
(b) What is the displacement (both magnitude & direction) of the center of mass of the three-piece system (with respect to the point the explosion occurs) 3.0s after the explosion?

 

[Doc Al]

During the explosion, momentum is conserved. Find the total momentum of all the pieces after the explosion. (Remember that momentum is a vector.) That total momentum equals the momentum the original object had before it exploded.

 

[M98Ranger]

To solve for the velocity and displacement of the package after an explosion, you will need to use principles of conservation of momentum and vector addition. The initial velocity of the package before the explosion can be found by adding the velocities of the three pieces using vector addition. This will give you the magnitude and direction of the initial velocity.

For part (b), you will need to calculate the center of mass of the three-piece system by finding the weighted average of the positions of each piece. Then, you can use the equation for displacement (displacement = velocity x time) to find the displacement of the center of mass after 3.0 seconds. Make sure to pay attention to the direction of the displacement, which will depend on the initial velocities of the pieces and the angle at which they were launched.

In summary, to solve for the velocity and displacement of the package after an explosion, you will need to use principles of conservation of momentum and vector addition for the initial velocity, and the equation for displacement for the center of mass after a certain time.