A ball of $1$ kg strikes a wedge of mass $4$ kg horizontally with a velocity of $10$ m/s. Just after collision velocity of wedge becomes $4 m / s$ . Friction is absent everywhere and collision is elastic. Select the correct alternative(s):

Speed of ball after collision is

6 m / s

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Speed of ball after collision is

8 m / s

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Impulse between ball and wedge during collision is

16 N s

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Impulse between ball and wedge during collision is

32 N s

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Solution

The correct option is A. Speed of ball after collision is $6 m / s$ .
Momentum in horizontal direction:
$P_{i} = m_{b} v_{b}$
$P_{i} = 1 \times (- 10) = - 10 k g m / s$
$P_{f} = m_{b} v_{b} + m_{w} v_{w}$
Let final velocity of ball $v_{f}$ and velocity of wedge $v_{w} = - 4 m / s$
$P_{f} = v_{f} + 4 \times (- 4)$
$P_{f} = v_{f} - 16$
Applying momentum conservation
$P_{i} = P_{f}$
$- 10 = v_{f} - 16$
$v_{f} = 6 m / s$
So the speed of the ball is $6 m / s$ and it is moving towards the right.

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