One ball of mass 0.600 kg traveling 9.00 m/s to the right collides head-on elastically with a second ball of mass 0.300 kg traveling 8.00 m/s to the left. After the collision, what are their velocities after collision? (Ans. -2.33 m/s (2.33 m/s to left) and 14.67 m/s (14.76 m/s to right))


Given:

Mass of first ball = m₁ = 0.6 kg
The initial velocity of the first ball
 to the right u₁ = 9.00 m/s  
Mass of the second ball = m₂ = 0.3 kg
Initial velocity of second ball = u₂ = - 8.00 m/s (-ve sign for opposite in direction to u₁)

To Find:

(a) Final velocity of mass m1 after collision = v = ?
(b) Final velocity of mass m2 after collision = v = ?


Solution:

(a) Final velocity of mass m1 after collision = v = ?

The 

formula to find the Final velocity of mass m1 is:

v = 
(m-m)u1m+m + 2mum+m

by putting values

v = (0.6kg-0.3kg)9.00ms0.6kg+0.3kg + 2x0.3kgx(-8.00ms)0.6kg+0.3kg

v = (0,6kg-0,3kg)9.00ms0.6kg+0.3kg - 2x0.3kgx(8.00ms)0.6kg+0.3kg

v = 3 m/s - 5.33 m/s

v = - 2.33 m/s -------------Ans.

The -ve sign shows the final velocity of mass m1 is opposite to its initial velocity i.e it is toward the left.

(b) Final velocity of mass m2 after collision = v₂ = ?


The formula to find the Final velocity of mass m is:

v = 
(m-m)um+m + 2mum+m

by putting values

v
 = (0.3kg-0.6kg)(-8.00ms)0.6kg+0.3kg + 2x0.6kgx(9.00ms)0.6kg+0.3kg

v = -(0.3kg-0.6kg)8.00ms0.6kg+0.3kg + 2x0.6kgx(9.00ms)0.6kg+0.3kg

v = -(-2.66) m/s + 12.0 m/s

v = 2.66 m/s + 12.0 m/s

v = 14.66 m/s -------------Ans.

The +ve sign shows the final velocity of mass m is opposite to its initial velocity direction i.e it is toward the right.



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