Question

an object at rest explodes into three pieces of equal mass. one move east at 20m/s a second moves southeast at 30m/s. what is the velocity of the thrid piece?

ANS: V3= 46.4 m/s

Answer 1

let the direction be as

initial momentum = 0
so, final momentum must be 0
let the mass of each piece be m

momentum of 1st piece = m*20 i
momentum of 2nd piece = m*(30*cos 45 i + 30*sin 45 j) = m*21.2 i + m*21.2 j
momentum of 1st piece + momentum of 2nd + momentum of 3rd = 0
m*20 i + m*21.2 i + m*21.2 j + m*v3 = 0
20 i + 21.2 i + 21.2 j + v3 = 0
v3 = - (41.2 i + 21.2 j) m/s

magnitude = sqrt (41.2^2 + 21.2^2) = 46.33 m/s

angle west of north = atan (41.2/21.2) = 62.8 degree