An object with total mass mtotal = 14.9 kg is sitting at rest when it explodes i

Question

An object with total mass mtotal = 14.9 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.8 kg moves up and to the left at an angle of 1 = 23° above the –x axis with a speed of v1 = 27.9 m/s. A second piece with mass m2 = 5.1 kg moves down and to the right an angle of 2 = 28° to the right of the -y axis at a speed of v2 = 20.9 m/s.

m3=5KG

What is the x-component of the velocity of the third piece?

What is the y-component of the velocity of the third piece?

Calculate the increase in kinetic energy of the pieces during the explosion.

Explanation / Answer

Since the object was at rest therefore the momentum after the explosion should be zero by the conservation of momentum.
therfore
The third particle should balance the momentum of the both 1 and 2 particle .
We resolve the momentum of the first and second particle along the x axis
Therfore we get X component velocity of mass 3
M3V3Cos(theta) = M1*V1Cos23 + M2V2Sin28
M3V3Cos(theta) = 4.8*27.9Cos23 + 5.1*20.9*Sin28 = 173.314
Therfore
V3Cos(theta) = 173.314/M3 = 173.314/5 = 34.66 m/s
Similarly for Y axis component we get
M3V3Sin(teta) = 4.8*27.9Sin23 - 5.1*20.9*cos28 = -41.787
V3Sin(theta) = - 41.787/5 = - 8.357 m/s
V3 = ((V3Sintheta)2 +( V3Cos(theta))2)1/2
V3 = 35.65 m/s
minus sign shows that our assumed direction is wrong.
therefore the m3 is in the fourth quadrant instead of 1 what we assumed.
But since we want magnitude so it will not affect our answer.
Increase in kinetic energy
1 particle = (1/2)mV12 = 0.5*4.8*27.92 = 1868.184 J
2 Particle = 0.5*5.1*20.92 = 1113.86 J
3 Particel = 0.5*5*(35.652) = 3177.88 J

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