Question

A running man has half the kinetic energy that a boy of half his mass has .the man speeds up by 1 m/s and then has the same kinetic energy as the boy. what are the original speeds of the man and the boy?

Answer 1

mass of man = m
mass of boy = m/2
velocity of man = u
velocity of boy = u'

Answer 2

Answer:

2.4 m/s and 4.8 m/s

Explanation:

Original speed of man = v

Speed of boy = V

Mass of man = m

Mass of boy = m/2

At original speed of man

Kinetic energy of man = 0.5 × Kinetic energy of boy

0.5mv² = 0.5 × 0.5(m/2)V²

v² = V²/4

v = V/2

V = 2v

When man speeds up by 1 m/s

Kinetic energy of man = Kinetic energy of boy

0.5m(v + 1)² = 0.5(m/2)V²

(v + 1)² = V²/2

(v + 1)² = (2v)²/2

(v + 1)² = 4v²/2

(v + 1)² = 2v²

v² + 2v + 1 = 2v²

v² - 2v - 1 = 0

v = 2.4 m/s

Speed of boy

V = 2v

= 2 × 2.4 m/s

= 4.8 m/s