Question

A running man has half the kinetic energy of that of a boy of half his mass. The man speeds up by 1m/s so as to have same K.E. as that of the boy. The original speed of the man will be:

• A. \( \sqrt{2} \, \text{m/s} \)
• B. \( \dfrac{1}{\sqrt{2}} \, \text{m/s} \)
• C. \( \sqrt{5} \, \text{m/s} \)
• D. \( \dfrac{1}{\sqrt{5}} \, \text{m/s} \)

Hint:

The kinetic energy is proportional to the square of the velocity. When the masses are different, speed adjustments are required to match the kinetic energies.

Answer 1

The Correct Option is A

Step 1: The kinetic energy \( K.E. \) of an object is given by \( K.E. = \dfrac{1}{2} mv^2 \), where \( m \) is the mass and \( v \) is the velocity.
Step 2: The kinetic energy of the man is half that of the boy, so the man’s speed must be \( \sqrt{2} \) times that of the boy’s speed. Therefore, the original speed of the man is \( \sqrt{2} \, \text{m/s} \).

Final Answer: \[ \boxed{\sqrt{2} \, \text{m/s}} \]