Question

The K.E. of a person is just half of K.E. of a boy whose mass is just half of that person. If person increases its speed by 1 m/*, then its K.E. equals to that of boy then initial speed of person was -

(1) (√2 + 1) m/*

(2) (2 + √2) m/*

(3) 2( √2 + 2) m/*

(4)

Answer 1

Correct Answer is: (1) (√2 + 1) m/s

Let initial speed of man of mass m be u then

KEman = 1/2 mu2 & KEboy = 2 × 1/2 mu2 = mu2

Now if man increases his speed by 1 m/*–1 then

KEman = 1/2 m (u + 1)2 = ' KEboy = mu2

⇒ u + 1/2 = √2