Visual SolutionEasy

Question

A ball of mass

2 \text{ kg}

moving at

4 \text{ m/s}

collides head-on with a stationary ball of mass

2 \text{ kg}

. If the collision is perfectly elastic, find the velocities of the two balls after the collision.

(A)

v_1 = 0,\; v_2 = 4 \text{ m/s}

(B)

v_1 = 2 \text{ m/s},\; v_2 = 2 \text{ m/s}

(C)

v_1 = 4 \text{ m/s},\; v_2 = 0

(D)

v_1 = -2 \text{ m/s},\; v_2 = 6 \text{ m/s}

Solution Path

Equal mass elastic collision: velocities exchange.

v_1 = 0

v_2 = 4 \text{ m/s}

. Both momentum and KE conserved.

01Question Setup

1/4

2 \text{ kg}

ball moving at

4 \text{ m/s}

hits a stationary

2 \text{ kg}

ball head-on. Perfectly elastic collision. Find velocities after collision.

v_1 = \;?, \quad v_2 = \;?

02Equal Mass ResultKEY INSIGHT

2/4

In a head-on elastic collision between equal masses where one is at rest, the velocities are exchanged: the moving ball stops, and the stationary ball moves with the initial velocity.

v_1 = 0, \quad v_2 = u_1 = 4 \text{ m/s}

03Verify with General Formula

3/4

Using the elastic collision formulas:

v_1 = \frac{m_1-m_2}{m_1+m_2}u_1 = \frac{2-2}{4}(4) = 0

v_2 = \frac{2m_1}{m_1+m_2}u_1 = \frac{4}{4}(4) = 4 \text{ m/s}

v_1 = 0, \quad v_2 = 4 \text{ m/s}

04Conservation Check

4/4

Momentum:

2(4) + 2(0) = 2(0) + 2(4) = 8 \text{ kg m/s}

\checkmark

. KE:

\frac{1}{2}(2)(16) = \frac{1}{2}(2)(16) = 16 \text{ J}

\checkmark

. Both conserved, confirming elastic collision.

\boxed{v_1 = 0, \; v_2 = 4 \text{ m/s}}

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