a ball moving with a speed 9m/s strikes an identical ball at rest , such that after the collisoins, the direction of each ball makes an angle of 30 degree with original line of motion.. find the speed of two balls after collisins
Let the mass of the balls be ‘m’.
Before collision net momentum along X axis is = 9m
Before momentum net momentum along Y axis is = 0
After collision, let the velocities of the balls be v1 and v2.
So, after collision the momentum along X axis is = mv1 cos30 + mv2 cos30
And the momentum along Y axis is = mv1 sin30 - mv2 sin30
Now, applying law of conservation of momentum,
mv1 cos30 + mv2 cos30 = 9m
=> v1 + v2 = 9/(cos30) = 10.39 ………..(1)
mv1 sin30 - mv2 sin30 = 0
=> v1 = v2 …………(2)
Using, (1) and (2),
v1 = v2 = 10.39/2 ≈ 5.2 m/s