Question

A running man has half k.E of that of boy of half of his mass .The man speeds up by m/s so as to have same k.E as that of boy .Find original speed

Answer 1

Complete question:

A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by 1 m/s. So as to have same kinetic energy as that of the boy. The original speed of the man is

A. √2 m/s

B. 1/(√2 - 1) m/s

C. 1/√2 m/s

D. 1/2√2 m/s

Answer:

The original speed is B. 1/(√2 - 1) m/s

Explanation:

Let mass of the man be M

Let speed of the man be v

The speed of the boy and man is given as:

1/2 Mv² = 1/2 [1/2 (M/2)v²] → (equation 1)

1/2 M(v + 1)² = 1/2 [(M/2)v²] → (equation 2)

On dividing equation (1) by (2), we get,

v²/(v + 1)² = 1/2

On taking square root on both sides, we get,

v/(v + 1) = 1/√2

√2v = v + 1

√2v - v = 1

v(√2 - 1) = 1

∴ v = 1/(√2 - 1) m/s