Question

A man racing with his son has half the kinetic energy of the son, who has half the mass of the father. The man speeds up by $1m/s$ and has the same kinetic energy as the son. What was the original speed of the man?

• A. 4.8 m/s
• B. 3.6 m/s
• C. 2.4 m/s
• D. 1.2 m/s

Answer 1

Answer: (C)

Let the velocity of father $=v_1$
According to the question, $v_i=\frac{1}{2}{K}_{\text{son }}$
Final velocity of the father $v_t=\left(v_1+1.0\right)m/s$
Then, $K_t=K_{\text{son }}{K}_i=\frac{1}{2}{K}_t$
$K_i=\frac{1}{2}\left[\frac{1}{2}m{\left(v_i+1.0\right)}^2\right]$
$K_i=\frac{1}{4}m\left(v_i^2+1+2v_i\right)$
$\frac{1}{2}m{v}_i^2=\frac{1}{4}m\left(v_i^2+1+2v_i\right)v_i^2$
$=\frac{v_i^2}{2}+\frac{1}{2}+v_i{v}_i^2-v_i-\frac{1}{2}=0$
$v_i^2-2v_i-1=0$
$v_i=2.4m/s$