00:01
Hello students, here given that a billiard ball player with the mass of billiard ball m1 hits the target and initial speed is u1.
00:18
Let us consider target mass is also m1.
00:22
This is before collision.
00:24
Then after collision, the ball will moves with making angle theta and target will makes angle.
00:44
Now we need to find the angle phi and also velocity of the target as well as ball after collision.
00:57
Let v1 be the velocity of the ball, v2 be the velocity of the target.
01:03
Using conservation of momentum, we can write before collision m1 u1 is equal to m1 v1 plus m1 v2.
01:15
From this we can write u1 is equal to v1 plus v2.
01:19
Squaring on both side, we get u1 square is equal to a plus b whole square that is b1 square plus v2 square plus 2 v1 v2.
01:30
Consider this as equation 1.
01:32
Next apply conservation of energy.
01:34
From that we write half m1 v1 square is equal to half m1 v1 square plus half m2 v2 square.
01:48
From this again here m2 is again m1, half m1 get cancelled, u1 square is equal to v1 square plus v2 square.
01:59
So from equation 2 and 1, we can write 2 v1 v2 is equal to 0.
02:08
2 v1 dot v2 can be written as 2 v1 v2 dot product is written as ab cos theta.
02:16
Here theta is between v1 and v2 is theta plus phi.
02:22
From this cos theta plus phi will be equal to 0.
02:28
We know that cos 90 is 0.
02:31
Hence theta plus phi is equated to 90 degree...