Question

a ball 'A' moving with speed of 90ms-1 collides directly with another identical ball 'B' moving with a speed V in opposite direction. 'A' comes to rest after the collision . if the coefficient of restitution is 0.8, the speed of 'B' before collision, V =

Answer 1

Answer:

the above given answer is zero but zero is not correct answer

Answer 2

The speed of 'B' before collision is 90 m/s.

Given

a ball 'A' moving with speed of 90ms-1

ball 'B' moving with a speed V in opposite direction

'A' comes to rest after the collision

The coefficient of restitution is 0.8.

To Find

We need to find the speed of B

Solution

Before collision

Velocity of A = $u_{1}$ = 90 m/s.

Velocity of B = $u_{2}$ = ?

Mass of A = m

Mass of B = m

After collision

Velocity of A = $v_{1}$ = 0 m/s

Velocity of B = $v_{2}$ m/s

According to the conservation of momentum,

          Inital momentum = final momentum

m $u_{1}$ - m   $u_{2}$= m $v_{1}$ + m $v_{2}$

m (  $u_{1}$ - $u_{2}$ ) = m (  $v_{1}$ +  $v_{2}$ )

    (  $u_{1}$ - $u_{2}$ ) = (  $v_{1}$ +  $v_{2}$ )

Substituing the values,

   90 -  $u_{2}$  = 0 +  $v_{2}$        equation → 1

We know that

       e = (  $v_{2}$ -  $v_{1}$ ) / (  $u_{1}$ - $u_{2}$ )

          = (  $v_{2}$ - 0 ) / ( 90 -   $u_{2}$ )

         =  $v_{2}$ / ( 90 -  $u_{2}$ )

          = 0.8 = $\frac{8}{10}$

10 $v_{2}$ = 720 - 8   $u_{2}$                           equation no → 2

Substituting value of  $v_{2}$   from equation 1

10 × ( 90 -  $u_{2}$ ) = 720 - 8   $u_{2}$

900 - 10  $u_{2}$ =  720 - 8   $u_{2}$

900- 720 =  - 8   $u_{2}$ + 10  $u_{2}$

180 = 2 $u_{2}$

$u_{2}$  = 90 m/s

The speed of 'B' before collision is 90 m/s.

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