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 5ms-1 his kinetic energy is 100% more than that of the boy. The initial velocity of the man is.​

Answer 1

the initial velocity of the man is 5 m/s

Answer 2

The initial velocity of the man will be 5m/s.

According to the question,

KE = kinetic energy

Given, Man = 1/2 KE of the boy

Man = v1 , m1

Boy = v2 , m2

⇒ m2 = m1/2

KE₁ ⇒ Man

KE₂⇒ Boy

To solve the above,

KE₁ =  1/2m1v1²

KE² = 1/2m2v2²

KE₁ = 1/2 KE₂

⇒ 1/2m1v1² = 1/2 × 1/2m2v2²

⇒ m1v1² = 1/2m2v2²

⇒ v1 = v2/2...( equation 1 )

(v1 + 5)m/s

⇒KE₁ = 1/2 m2 (v1 + 5)²

⇒KE₁ = KE₂ + 100/100 × KE₂

⇒KE₁ = 2KE₂

⇒1/2 m1(v1 + 5)² = 2 × 1/2 × m2 × v2²

⇒(v1 + 5)² = (2v1)²

⇒v1 + 5 = 2v1

⇒2v1 - v1 = 5

⇒ v1 = 5m/s

Therefore the initial velocity of the man is 5m/s.

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