Question

A steel ball A of mass 20.0 kg moving with a speed of 2.0 ms−1 collides with another ball B of mass 10.0 kg which is initially at rest. After the collision A moves off with a speed of 1.0 ms−1 at an angle of 30º with its original direction of motion. Determine the final velocity of B.

Answer 1

Solution to Question #87899, Physics / Mechanics | Relativity | for completion

A steel ball A of mass $20.0\mathrm{kg}$ moving with a speed of $2.0~\mathrm{ms}^{-1}$ collides with another ball B of mass $10.0\mathrm{kg}$ which is initially at rest. After the collision A moves off with a speed of $1.0~\mathrm{ms}^{-1}$ at an angle of $30{}^{\circ}$ with its original direction of motion. Determine the final velocity of B.

Solution:

Assume the collision is inelastic

Now apply law of conservation of momentum in $x$ direction

$$\begin{array}{l} m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2} \\ 20 \times 2 + 10 \times 0 = 20 \times 1 \times \cos 30{}^{\circ} + 10 \times v_{2} \\ \end{array}$$

Solve for $v_{2}$

$$v_{2} = 2.268~\mathrm{m/s}$$

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