Question

A plate falls vertically to the floor and breaks up into three pieces, which slide along the floor. Immediately after the impact, a 390-g piece moves along the x-axis with a speed of 2.00 m/s and a 410-g piece moves along the y-axis with a speed of 1.50 m/s. The third piece has a mass of 100 g. In what direction does the third piece move? You can neglect any horizontal forces during the crash.

Answer 1

Mass of the first plate m1 = 390g = 0.39kg

Mass of the second plate m2 = 410 g = 0.41 kg

Velocity of the first plate v1 = 2.0 m/s i

Velocity of the second plate v2 = 1.50 m/s j

Mass of the third plate m3 = 100 g = 0.1 kg

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From law of conservation of momentum

along x-axis

m1v1 + m3v3 = 0

the velocity of mass m3 along axis

v3 = - m1v1/m3 = - (0.39 kg)(2.0 m/s) / 0.1 kg

=- 7.8 m/s i

alon y-axis

m2v2 + m3v3 =0

then velocity of mass along y-axis

v3 = - m2v2/m3

= - (0.41 kg)(1.5 m/s) / 0.1 kg

=- 6.15 m/s i

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Therefore the speed of third mass

v3 = √(7.8m/s)2 + (6.15 m/s)2

= 9.93m/s

and the angle θ = tan-1(6.15 /7.8)

= 38.25

Since both component in negative axis then

Therefore the angle θ = 180 +38.25 = 218.25 deg from +x-axis.