Question

A running man has half the kinetic energy that a boy
of half his mass has. The man speeds up by 1.0 meter/
sec and then has the same kinetic energy as the boy.
What were the original speeds of man and boy?
(A) 2.4 m/sec, 4.8m/sec
(B) 4.8m/sec, 2.4m/sec
(C) 4.2 m/sec, 8.4m/sec
(D) 8.4m/sec, 4.2m/sec​

Answer 1

Answer:

(A) 2.4 m/sec, 4.8m/sec

Explanation:

let the man speed be v and that of the boy be c

then

1/2mv² = 1/8 mc²

1/2 m(v+1)² = 1/4mc²

(v+1 ÷v)² = 2

v = √2 +1 = 2.4 m/sec

c = 2v = 4.8 m/sec

choose ans. (A)

(A) 2.4 m/sec, 4.8m/sec