# An object with total mass mtotal = 15.8 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 θ1 = 18° above the –x axis with a speed of v1 = 27.6 m/s. A second piece with mass m2 = 5.4 kg moves down and to the right an angle of θ2 = 23° to the right of the -y axis at a speed of v2 = 21.5 m/s.

a. What is the magnitude of the final momentum of the system (all three pieces)?

b. What is the mass of the third piece?

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

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

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

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

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1. (a) 0 kg*m/s

(b) (15.8 - 4.5 - 5.4)kg
= 5.9 kg

(c) 0 = [4.5*27.6*cos162º + 5.4*21.5*cos293º + 5.9*V*cosΘ3] kg·m/s
for V in m/s

horizontal component V*cosΘ3 = 72.8/5.9 m/s
= 12.3 m/s

(d) 0 = [4.5*27.6*sin162º + 5.4*21.5*sin293º + 5.9*V*sinΘ3] kg·m/s
for V in m/s

vertical component V*sinΘ3 = 68.4/5.9 m/s
= 11.6 m/s

(e) 0 m/s

(f) 0.5 * [4.5*27.6² + 5.4*21.5² + 5.9*(12.3² + 11.6²)] J
= 3810 J

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