Question

A cracker of mass 100g explodes into two pieces of equal mass show that these two pieces of the cracker fly in opposite direction.

Answer 1

the total momentum =constant
P = M 

for V₀
M = 100 g
 V₀ = 0. So, P = 0.

and
After the explosion,
P = m1 x V1 + m2 x V2

where m1 = m2 = M / 2. Putting the value
(M / 2) x V1 + (M / 2) x V2 = 0

V1 + V2 = 0
V1 = - V2,
so they fly in opposite directions.

Answer 2

In a closed system , total momentum P = constant
M= 100, V= 0
∴ P = MV
P = 100 X 0 = 0
After explosion,
P = m1v1+ m2v2, where m1 = m2 = M/2
so P = M/2 x v1 + M/2 x v2
0 = M/2 (v1 + v2)
0 = v1 + v2
v1 = -v2
this shows that the two pieces of the cracker fly in opposite direction