A 3 kg bomb explodes into 3 equal pieces A, B and C. A
flies with a speed of 40 m/s and B with a speed of 30 m/s
making an angle of 90° with the direction of A. The angle
made by the direction of C with that of A is
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Linear momentum is conserved before and after explosion.
The bomb is at rest before it explodes. So, the initial momentum is zero.
Let's say the piece A moves along positive x-axis, and the piece B along positive y-axis. And let's assume that the piece C is moving at an angle of θ with the negative x-axis at a speed of v.
Conserving along the x-axis
0 = 1 ( 40 )-1 ( v cos θ)
vcosθ = 30
From these two equations,
tanθ = 3/4
cosθ = 4/5
So,piece C makes an angle of π-cosθ-1 4/5with piece A
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