An object with total mass m total = 15.4 kg is sitting at rest when it explodes

Question

An object with total mass mtotal = 15.4 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.5 kg moves up and to the left at an angle of 1 = 22° above the –x axis with a speed of v1 = 26.1 m/s. A second piece with mass m2 = 5.3 kg moves down and to the right an angle of 2 = 27° to the right of the -y axis at a speed of v2 = 23.7 m/s.

3-

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

4-

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

5-

What is the magnitude of the velocity of the center of mass of the pieces after the collision?

6-

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

Explanation / Answer

3)    0 = - 4.5 * 26.1 * cos22 + 5.3 * 23.7 * sin27 + 5.6 * Vx

=> Vx =   9.263 m/sec

4)    0 = 4.5 * 26.1 * sin22 - 5.3 * 23.7 * cos27 + 5.6 * Vy

=> Vy =   12.13 m/sec

5)    system momentum still = 0, so velocity of centre of mass = 0 m/sec

6)   increase in kinetic energy = 1/2 * 4.5 * 26.12 + 1/2 * 5.3 * 23.72 + 1/2 * 5.6 * 15.262

                                                         =   3673.23 J

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