Question

A rocket used for fireworks explodes just when it reaches its highest point in a vertical trajectory. It initially bursts into three fragments with masses of m, 3m, and 4m, each of these to explode slightly later. If the 4m fragment falls vertically with an initial velocity of 8 m/s, and the 3m fragment is ejected with a velocity of 10 m/s at an angle of 30° above the horizontal, find the velocity of the third fragment.

Answer 1

Here,

let the velocity of third is v

as the initial momentum is zero at the highest point

m * v + 4m * (-8 j) + 3m * (10 * cos(30) i + sin(30) j) = 0

v + 4 (-8 j) + 3 (10 * cos(30) i + 10 * sin(30) j) = 0

solving

v = 17 j - 26 i

v = 31 m/s at 33.2 degree above horizontal

the velocity of the third fragment is 31 m/s at 33.2 degree above horizontal