Question

A running boy has the same kinetic energy as that of a man of twice his mass. If the speed of the boy is \(14.14\ \text{m s}^{-1}\), the speed of the man is

• A. \(1.414\ \text{m s}^{-1}\)
• B. \(0.25\ \text{m s}^{-1}\)
• C. \(10\ \text{m s}^{-1}\)
• D. \(3\sqrt{2}\ \text{m s}^{-1}\)
• E. \(0.5\ \text{m s}^{-1}\)

Hint:

If kinetic energies are equal, compare \(mv^2\) directly instead of writing \(\frac12\) every time.

Answer 1

The Correct Option is C

Let the boy's mass be \(m\), so the man's mass is \(2m\). Equal kinetic energies: \[ \frac12 m(14.14)^2=\frac12 (2m)v^2 \] \[ (14.14)^2 = 2v^2 \] Since \[ 14.14 \approx 10\sqrt{2} \] \[ (10\sqrt{2})^2=2v^2 \] \[ 200=2v^2 \Rightarrow v^2=100 \Rightarrow v=10 \] Hence, \[ \boxed{(C)\ 10\ \text{m s}^{-1}} \]