A 2.25 kg stationary package explodes into three parts that then slide across a

Question

A 2.25 kg stationary package explodes into three parts that then slide across a frictionless floor. The package had been at the origin of a coordinate system. Part 1 has mass m1 = 0.500 kg and velocity (10.0ihat + 12.0jhat) m/s. Part 2 has mass m2 = 0.750 kg, a speed of 12.0 m/s, and travels at an angle 115° (counterclockwise from the positive direction of the x axis.)

(a) What is the speed of part 3?
(b) In what direction does it travel? ________° counterclockwise from the positive direction of the x axis

Explanation / Answer

Total Mass = 2.25kg
Mass of part1 (m1) = 0.5kg, Mass of part2 (m2) = 0.75kg

Hence Mass of part 3(m3) = Total mass - m1 - m2

= 2.25-0.5-0.75 = 1kg

Given Velocity of part1 (v1)= 10i + 12j

velocity of part2 (v2) = 12m/s at an angle 115°(Counter clockwise direction)

Hence v2 = 12(cos115 i + sin115j) = 12(-0.4226i + 0.9063j) = -5.0714i+10.8757j

From law of conservation of momentum, m1 v1 + m2 v2 + m3 v3 =0

1*v3 = -0.5(10i + 12j) -0.75*(-5.0714i+10.8757j)

---> v3 = - 1.1965 i -14.1568 j = 14.2073 at an angle 265.1690o

a) Speed of part 3 = 14.2073 m/s

b) It travels at an angle 265.1690o counterclockwise from the positive direction of the x axis

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