Question

A man of mass 50 kg starts moving on the earth and acquires a speed 1.8 m/s. With what speed does the earth recoil? Mass of earth = 6 × 10²⁴ kg.

Answer 1

By the law of conservation of linear momentum, we have:
$m_1{v}_1=m_2{v}_2$
Here, m₁ and v₁ are the mass and velocity of the man respectively, and m₂ and v₂ are the mass and velocity of the Earth respectively.

$$\begin{gathered} \Rightarrow 50\times 1.8=6\times {10}^{24}\times v_2 \\ \therefore v_2=\frac{50\times 1.8}{6\times {10}^{24}}=15\times {10}^{-24}\mathrm{m}/\mathrm{s} \\ \Rightarrow v_2=1.5\times {10}^{-23}\mathrm{m}/\mathrm{s} \end{gathered}$$
Hence, the earth recoils with a speed of 1.5 × 10⁻²³ m/s.