Question

A mother has four times the mass of her young son. Both are running with the same kinetic energy. What is the ratio v_son /v_mother of their speeds?

Short answer

The ratio isv_son /v_{mother =} 2:1

Step-by-step solution

Given information

A mother has four times the mass of her young son.

Both are running with the same kinetic energy

Explanation

The kinetic energy is calculated by $K.E=0.5\times m\times V^2....................\left(1\right)$

Use equation (1) to calculate the kinetic energy of son and mother and find the ratio

Lets assume

Suppose K . E_son is the kinetic energy for son and

K . E_mother s the kinetic energy for mother and it is given that both have same kinetic energy so,

$$\begin{gathered} K·E_{son}=K·E_{mother} \\ 0.5\times M_{\text{son}}\times V_{\text{son}}{}^2=0.5\times M_{\text{mother}}\times V_{\text{mother}}^2 \end{gathered}$$

$$\begin{gathered} M_{\text{mother}}=4\times M_{\text{son}} \\ \left(V_{\text{son}}{}^2/{V_{\text{mother}}}^2\right)=M_{\text{mother}}/M_{\text{son}} \end{gathered}$$

Substitute the given values

$$\begin{gathered} {\left(V_{\text{son}}/V_{\text{mother}}\right)}^2=4/1 \\ Takesquarerootbothsides \\ \left(V_{\text{son}}/V_{\text{mother}}\right)=2/1=2:1 \end{gathered}$$