Question

A 4.0-kilogram ball moving at 8.0 m/s to the right collides with a 1.0-kilogram ball at rest. After the collision, the 4.0-kilogram ball moves at 4.8 m/s to the right. What is the velocity of the 1-kilogram ball?

Answer 1

Answer: The velocity of ball having less mass is 12.8 m/s

Explanation:

To calculate the velocity of the ball having less mass after the collision, we use the equation of law of conservation of momentum, which is:

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

where,  

$m_1$ = mass of ball 1 = 4.0 kg

$u_1$ = Initial velocity of ball 1 = 8.0 m/s

$v_1$ = Final velocity of ball 1 = 4.8 m/s

$m_2$ = mass of ball 2 = 1.0 kg

$u_2$ = Initial velocity of ball 2 = 0 m/s

$v_2$ = Final velocity of ball 2 = ?

Putting values in above equation, we get:

$(4.0\times 8.0)+(1.0\times 0)=(4.0\times 4.8)+(1.0\times v_2)\\\\v_2=\frac{32-19.2}{1}=12.8m/s$

Hence, the velocity of ball having less mass is 12.8 m/s

Answer 2

Its about momentum. Momentum (p)=mass(m)xvelocity(v)
So for the first ball P=4x8=32kgm/s
For the second the momentum is zero as it is still.
So overall momentum its 32kgm/s
Momentum has to be conserved
After the collision the momentum of the 4kg ball is 4x4.8=19.2kgm/s
As momentum is conserved 32-19.2=12.8kgm/s remaining
So rearrange for velocity so v=p/m=12.8/1=12.8m/s for the 1kg ball