Question

a man weighting 80 kg is standing in a trolly weighting 320 kg. the trolly is resting on frictionless horizontal rails.if man starts walking on the trolly with a speed of 1m/s then after 4 sec his displacement relative to the ground will be

Answer 1

Answer on Question #34639 – Physics – Mechanics | Relativity

A man weighting $80\,\mathrm{kg}$ is standing in a trolley weighting $320\,\mathrm{kg}$. The trolley is resting on frictionless horizontal rails. If man starts walking on the trolley with a speed of $1\,\mathrm{m/s}$ then after 4 sec his displacement relative to the ground will be...

**Solution.**

$$m_1 = 80\,\mathrm{kg} - \text{man weight}$$ $$m_2 = 320\,\mathrm{kg} - \text{trolley weight}$$

Change in impulse for the total system must be zero:

$$v_1 = 1\,\frac{m}{s} - \text{velocity (man)}$$ $$v_2 - \text{velocity (trolley)}$$ $$p = mv - \text{impulse}$$

So

$$p_1 = p_2$$ $$m_1 v_1 = -m_2 v_2$$ $$80 \cdot 1 = -320 v_2$$

Express $v_2$ from the equation:

$$v_2 = -\frac{80}{320} = -0.25\,\frac{m}{s}$$

Man’s effective velocity is:

$$V = v_1 - v_2 = 1 - 0.25 = 0.75\,\frac{m}{s}$$

After 4 seconds, he travelled the distance:

$$S = Vt = 0.75 \cdot 4 = 3\,\mathrm{m}$$

Answer: $3\,\mathrm{m}$

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