Question

The kinetic energy of a man is half that of a boy whose mass is half that of the man. When the man speeds up by 5 m/s, his kinetic energy doubles that of the boy’s kinetic energy. What is the initial velocity of the man?

(a) 5 m/s

(b) 10 m/s

(c) 15 m/s

(d) 20 m/s

I have been asked this question in quiz.

This question is from Kinetic Energy in division Work, Energy and Power of Physics – Class 11

Answer 1

Right answer is (a) 5 m/s

The explanation: The kinetic energy of man (initial) = KE

 = KE’/2

The kinetic energy of man (final) = 2 x KE’

The kinetic energy of boy = KE’

Mass of man = M

Mass of boy = m

 = M/2

v = Initial velocity of man

v’ = Initial velocity of boy

(1/2) x M x v^2  = (1/2) x m x v’^2

 = (1/2) x M/2 x v’^2

Therefore; v = v’/2^0.5

(1/2) x M x (v+5) ^2  =  2 x (1/2) x m x v’^2

 = 2 x (1/2) x M/2 x (2 x v^2)

(v+5) ^2 = 4 x v^2

v + 5 = 2 x v

v = 5m/s.