V1ix = initial velocity of first ball in X-direction = 2 m/s
V1iy = initial velocity of first ball in Y-direction = 0 m/s
V1fx = final velocity of first ball in X-direction = V1 Cos30
V1fy = final velocity of first ball in Y-direction = V1 Sin30
V2ix = initial velocity of second ball in X-direction = 0 m/s
V2iy = initial velocity of second ball in Y-direction = 0 m/s
V2fx = final velocity of second ball in X-direction = V2 Cos
V2fy = final velocity of first ball in Y-direction = - V2 Sin
Using conservation of momentum Along X-direction :
m1 V1ix + m2 V2ix = m1 V1fx + m2 V2fx
m1 (3) + m2 (0) = m1 V1 Cos30 + m2 V2 Cos
V1 Cos30 + V2 Cos = 3
V2 Cos = 3 - V1 Cos30 Eq-1
Using conservation of momentum Along Y-direction :
m1 V1iy + m2 V2iy = m1 V1fy + m2 V2fy
2 (0) + 2 (0) = 2 (V1 Sin30) + 2 (- V2 Sin)
V2 Sin = V1 Sin30 Eq-2
Squaring Eq-1 and Eq-2 and adding
V22 Cos2 + V22 Sin2 = (3 - V1 Cos30 )2 + V21 Sin230
V22 = 9 + V21 Cos230 - 6 V1 Cos30 + V21 Sin230
V22 = 9 + V21 - 6 V1 Cos30 Eq-3
since the collision is elastic
(0.5) m1 (3)2 + (0.5) m2 (0)2 = (0.5) m1 (V1)2 + (0.5) m2 (V2)2
9 = (V1)2 + (V2)2
V22 = 9 - V12 Eq-4
Using eq-3 and Eq-4
9 - V12 = 9 + V21 - 6 V1 Cos30
V1= 2.6 m/s
from Eq-4
V22 = 9 - V12 = 9 - (2.6)2 = 2.24
V2 = 1.5 m/s
Using Eq-2
V2 Sin = V1 Sin30
1.5 Sin = (2.6) (0.5)
= 60.5
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