Two bodies of masses 5 kg and 10kg approach each other with velocities 10 m/s and 5 m/s respectively. Calculate their velocities after collision, assuming the collision to be elastic.
Answers
Answer:
The 10kg ball will travel along X−axis with a velocity of 33.33m/s & the 20kg ball will travel along +X axis with a velocity of6.67m/s.
Explanation:
Let the velocities of 10kg & 20kg ball before collision are u1 =20m/s(+X axis) & u2 = −20m/s( -X axis) and after collision v1 & v2
respectively. Than by the principal of momentum conservation: -
m1u1 +m2 u2 =m 1 v1 +m2 v 2
(10×20)+(20×(−20))=(10×v 1 )+(20×v 2 )
v 1 +2v 2 =−20 ---------------------(i)
Since the collision is perfectly elastic (e = 1)
e=(v 2 −v 1 )/(u 1 −u 2 )=1
v 2 −v 1 =20−(−20)=40------------------------(ii)
On adding (i) & (ii): -
3v 2 =20
44v 2 =6.67m/s
v 1 =6.67−40=−33.33m/s
The 10kg ball will travel along X−axis with a velocity of 33.33m/s & the 20kg ball will travel along +X axis with a velocity of 6.67m/s.