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 = 28 m/s. A second piece with mass m2 = 5.2 kg moves down and to the right an angle of 2 = 28° to the right of the -y axis at a speed of v2 = 21 m/s.
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

m3 = 14.9 -(4.8 + 5.2)

= 4.9 kg

a) Apply conservation of momentum in x-direction

initial momenmtum = final momentum

0 = -m1*v1*cos(theta1) + m2*v2*cos(theta2) + m3*v3x

==> v3x = (m1*v1*cos(theta1) - m2*v2*cos(theta2))/m3

= (4.8*28*cos(20) - 5.2*21*cos(28))/4.9

= 6.1 m/s

b) Apply conservation of momentum in y-direction

initial momenmtum = final momentum

0 = m1*v1*sin(theta1) - m2*v2*sin(theta2) + m3*v3y

==> v3y = (-m1*v1*sin(theta1) + m2*v2*sin(theta2))/m3

= (-4.8*28*sin(20) + 5.2*21*sin(28))/4.9

= 1.1 m/s

c) so, v3 = sqrt(v3x^2 + v3y^2)

= sqrt(6.1^2 + 1.1^2)

= 6.2 m/s

increase in kinetic energy of the pieces = 0.5*m1*v1^2 + 0.5*m2*v2^2 + 0.5*m3*v3^2

= 0.5*4.8*28^2 + 0.5*5.2*21^2 + 0.5*4.9*6.2^2

= 3122 J

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