An object with total mass mtotal = 17.7 kg is sitting at rest when it explodes i

Question

An object with total mass mtotal = 17.7 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.9 kg moves up and to the left at an angle of ?1 = 18° above the –x axis with a speed of v1 = 27.1 m/s. A second piece with mass m2 = 5.4 kg moves down and to the right an angle of ?2 = 23° to the right of the -y axis at a speed of v2 = 20.2 m/s.
What is the y-component of the velocity of the third piece?
What is the magnitude of the velocity of the center of mass of the pieces after the collision?
Calculate the increase in kinetic energy of the pieces during the explosion

Explanation / Answer

As the object is at rest, so Initial momentum = 0 And the sum of x and y component must be equal to zero, so Mass m1 = 4.9 kg moves up and to the left at an angle of ?1 = 18° above the –x axis with a speed of v1 = 27.1 m/s. The x-component of the velocity is negative and the y-component is positive x = 4.9 * -27.1 * cos 18° y = 4.9 * +27.1 * sin 18° Mass m2 = 5.4 kg moves down and to the right an angle of ?2 = 23° to the right of the -y axis at a speed of v2 = 20.2 m/s. The x-component of the velocity is positive and the y-component is negative. x = 5.4 * +20.2 * cos 23° y = 5.4 * -20.2 * sin 23° Mass of 3rd piece = 17.7 – (4.9 + 5.4) = 7.4 kg x = 7.4 * cos ? y = 7.4 * sin ? Sum of x-components = 4.9 * -27.1 * cos 18° + 5.4 * +20.2 * cos 23° + 7.4 * cos ? = 0 7.4 * cos ? = 4.9 * +27.1 * cos 18° + 5.4 * -20.2 * cos 23° (i) Sum of y-components = 4.9 * +27.1 * sin 18°+ 5.4 * -20.2 * sin 23° + 7.4 * sin ? = 0 7.4 * sin ? = 4.9 * -27.1 * sin 18°+ 5.4 * +20.2 * sin 23° (ii) Divide Eq. #2 by Eq. #1 and calculate the tangent of ? and then ?. Tan ? = Use the value of ? to determine the magnitude of the velocity of the 3rd piece.

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