A suspicious package slides on a frictionless surface and then explodes into thr

Question

A suspicious package slides on a frictionless surface and then explodes into three chunks of equal mass. Chunk A has a velocity of 13.1 m/s due north. Chunk B has a velocity of 3.70 m/s and is directed 29.1 degrees south of west. Chunk C has a velocity of 3.70 m/s and is directed 29.1 degrees south of east.

Part A

Find the magnitude of the velocity of the package before it exploded.

Part B

Find the direction of the package before it exploded. Assume that east is zero degrees and the angle increases counterclockwise.

Explanation / Answer

here,

let the mass of each chunkes be m

velocity of chunk A , vA = 13.1 m/s j

velocity of chunk B , vB = 3.7 * ( - cos(29.1) i - sin(29.1) j)

vB = - 3.23 i m/s - 1.8 m/s j

velocity of chunk C , vC= 3.7 * ( cos(29.1) i - sin(29.1) j )

vC = 3.23 m/s i - 1.8 m/s j

let the initial velocity be u

using conservation of momentum

3*m*u = m*vA + m*vB = + m*vC

3*u = 13.1 m/s j- 3.23 i m/s - 1.8 m/s j + 3.23 m/s i - 1.8 m/s j

u = 9.5 m/s j

the magnitude of the velocity of of the package before it explodes is 9.5 m/s

the direction is 90 degree from east in cloxkwise direction

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