Question

A missile breaks up into two pieces, one of which has a mass of 230 grams and flies off along the positive x-axis with a speed of 84.3 m/s. A second piece has a mass of 390 grams and flies off along the negative y-axis with a speed of 38.1 m/s. What is the magnitude and angle (in degrees) of the momentum of the missile right before it breaks up?

Please show full work clearly.

Answer 1

mass of the missile = 230 + 390 = 620 g

let the speed of the missile before breaking be Vx and Vy in x and y-direction respectively

Conserving the momentum in x-direction we have

620Vx = 230*84.3

Vx = 31.27 m/s

conserving the momentum in y-direction

620 Vy = 390*-38.1

Vy = -23.96 m/s

Magntiude of V = sqrt(Vx^2 + Vy^2)

               = sqrt( 31.27^2 + 23.96^2) = 39.4 m/s

magntiude of momentum = mv = 0.62*39.4 = 24.42 kg m/s

angle = tan^1-(23.96 / 31.27) = 37.46^o below the x-axis in clockwise direction