A ball A moving with momentum 2ˆ 6 ˆ i j collides with another identical moving ball B with momentum 4 ˆ j and momentum of ball B after collision is 2 ˆj . The coefficient of restitution in the collision is 15 x . Find the value of x.
Answers
Given info : A ball A moving with momentum 2i + 6j collides with another identical moving ball B with momentum 4 j and momentum of ball B after collision is 2 j.
To find : the coefficient of restitution is 15x then find the value of x.
solution : balls are identical means masses are equal. Let mass of each ball is m.
initial velocity of ball A = (2i + 6j)/m
[ momentum/mass = velocity as you know it ]
initial velocity of ball B = 4j/m
final velocity of ball B = 2j/m
from law of conservation of linear momentum,
initial momentum = final momentum
⇒(2i + 6j) + 4j = P + 2j
⇒2i + 8j = P
so, final velocity of ball A = (2i + 8j)/m
Now coefficient of restitution = relative velocity after collision/relative velocity before collision.
= |(2i + 8j - 2j)/m|/|(2i + 6j - 4j)/m|
= |2i + 6j|/|2i + 2j|
= √40/√8
= √5
given , coefficient of restitution is 15x
so, 15x = √5
⇒x = 1/3√5
Therefore the value of x is 1/3√5