Question

A mother has four times the mass of her young son. Both are running with the same kinetic energy. Part A What is the ratio vs/vm other of their speeds

Answer 1

Answer: 2:1

Explanation:

Given

Mother has four times the mass of young son

If they possess same kinetic energy then $K_m=K_s$

$\Rightarrow K_m=\dfrac{1}{2}\times m_m\times v^2_m$

$\Rightarrow K_s=\dfrac{1}{2}\times m_s\times v^2_s$

Equate the energy

$\Rightarrow \dfrac{1}{2}\times m_m\times v^2_m=\dfrac{1}{2}\times m_s\times v^2_s\\\\\Rightarrow \dfrac{1}{2}\times 4m_s\times v^2_m=\dfrac{1}{2}\times m_s\times v^2_s\\\\\Rightarrow 4 v^2_m=v^2_s\\\\\Rightarrow \dfrac{v_s}{v_m}=\sqrt{4}\\\\\Rightarrow \dfrac{v_s}{v_m}=2$

Thus, the ratio of speed is 2:1.