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 $1\, m/s$ 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, $K_{t}=K_{\text {son }} K_{i}=\frac{1}{2} K_{t}$
$K_{i}=\frac{1}{2}\left[\frac{1}{2} m\left(v_{i}+1.0\right)^{2}\right]$
$K_{i}=\frac{1}{4} m\left(v_{i}^{2}+1+2 v_{i}\right)$
$\frac{1}{2} m v_{i}^{2}=\frac{1}{4} m\left(v_{i}^{2}+1+2 v_{i}\right) v_{i}^{2}$
$=\frac{v_{i}^{2}}{2}+ \frac{1}{2}+v_{i} v_{i}^{2}-v_{i}-\frac{1}{2}=0$
$v_{i}^{2}-2 v_{i}-1=0$
$v_{i}=2.4\, m / s$