b) What is the direction of the third piece? An m = 6.30-kg clay ball is thrown

Question

b) What is the direction of the third piece?

An m = 6.30-kg clay ball is thrown directly against a perpendicular brick wall at a velocity of 22.0 m/s and shatters into three pieces, which all fly backward, as shown in the figure. The wall exerts a force on the ball of 2620 N for 0.110 s. One piece of mass m1 = 2.30 kg travels backward at a velocity of 10.6 m/s and an angle of = 32.0 above the horizontal. A second piece of mass m2 = 1.30 kg travels at a velocity of 8.10 m/s and an angle of 28.0 below the horizontal. a) What is the velocity of the third piece? b) What is the direction of the third piece?

Explanation / Answer

Here , we will use conservation of momentum ,

mass m3 = (6.30 - 2.30 - 1.3)

m3 = 2.7 Kg

Now , balacing momentum in y -direction

2.7*Vy + 2.30*sin(32)*10.6 - 1.3*sin(28)*8.10 = 0

Vy = -2.95 m/s

Now , balacing momentum in x - direction

2.7*Vx + 2.30*cos(32)*10.6 + 1.3*cos(28)*8.10 = -22*6.30+2620*0.11

solving for Vx

Vx = 45.12 m/s

therefore ,

Velocity V3 = sqrt(Vx^2 + Vy^2)

V3 = sqrt(2.95^2 + 45.12^2)

V3 = 45.22 m/s

the velocity of third piece is 45.22 m/s

b)

angle = arctan(-2.95/45.12)

angle = 3.71 degree below horizontal

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