Two identical balls, A and B, undergo a perfectly elastic two-dimensional collision. Initially A is moving with a speed of 10ms−1 and B is at rest. Due to collision, A is scattered through an angle of 30°. What are the speeds of A and B after the collision?
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☆Given:
❇ Two identical balls A and B undergoes 2d collision
❇ A is moving with a speed of 10 ms-1 , B- rest
❇ Due to collision A is scattered at 30°
☆To find:
● speeds of A and B after collision =?
☆Solution:
m1 = m2=m ( since they are identical balls)
u1 = 10 ms-1 ( Inital velocity )
Theta = 30° , inital velocity (V1)=? , final velocity (V2) = ?
ϕ = ?
Along x - axis;
m u 1 = mv1 cos theta + mv2 cosϕ
( m gets cancelled )
10= v1 root 3
------------ + v2 cosϕ
2
Along y-axis;
0 = mu1 sin theta - mv2 sin ϕ
u1 sin theta = v2sin ϕ
1/2 m u ^2 = 1/2 m V1 ^2 + 1/2 m V2^2
V1^2 + V2^2 = 100
u2 = 20/4 = 5 ms-1
u1 = root 3 * 5 = 1.732 × 5 = 8.6 ms-1
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