MA ball explodes into three pieces. Two pieces of equal mass fly off to the nort
ID: 1356312 • Letter: M
Question
MA ball explodes into three pieces. Two pieces of equal mass fly off to the north and to the east with a speed of 28 m/s each. Find the velocity of the third piece given that its mass is equal to the sum of the other two pieces. MA ball explodes into three pieces. Two pieces of equal mass fly off to the north and to the east with a speed of 28 m/s each. Find the velocity of the third piece given that its mass is equal to the sum of the other two pieces. MA ball explodes into three pieces. Two pieces of equal mass fly off to the north and to the east with a speed of 28 m/s each. Find the velocity of the third piece given that its mass is equal to the sum of the other two pieces.Explanation / Answer
mass of original piece = Ma
mass of two equal pieces = m = Ma/4
mass of third piece = m' = Ma/2
consider east-west direction as X-axis and north-south direction as Y-axis
Consider the x-direction
initial momentum = 0
velocity of one of two equal piece along X-direction = 28 m/s
Vx = speed of third particle along X-axis
Using conservation of momentum :
0 = m (28) + m' Vx
0 = ( Ma/4) (28) + (Ma/2) Vx
Vx = - 3.5 m/s along negative X-direction (west)
Consider the Y-direction
initial momentum = 0
velocity of one of two equal piece along Y-direction = 28 m/s
Vy = speed of third particle along Y-axis
Using conservation of momentum :
0 = m (28) + m' Vx
0 = ( Ma/4) (28) + (Ma/2) Vy
Vy = - 3.5 m/s along negative Y-direction (south)
Net velocity = V = sqrt (Vx2 + Vy2) = sqrt ((-3.5)2 + (-3.5)2) = 4.95 m/s
direction : along west-south direction
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