John's mass is half the mass of Jill. They both start walking and John moves twice as fast as Jill. What is the ratio of the kinetic energy of Jill to the kinetic energy of John?

Question

Quizplus · Accepted Answer

Let's assume the mass of Jill to be 'm'. Therefore, the mass of John would be 0.5m.
Let's assume the speed of Jill to be 'v'. Therefore, the speed of John would be 2v.
Now, Kinetic Energy is given by 0.5*m*v^2
Let's calculate the KE of Jill and John and take their ratio:

KE of Jill = 0.5*m*v^2
KE of John = 0.5*0.5m*(2v)^2 = 2*0.5*m*v^2 = m*v^2

Ratio of KE of Jill to KE of John = KE of Jill/ KE of John = {0.5*m*v^2}/{m*v^2} = 0.5/1 = 1/2

Hence, the ratio of the Kinetic Energy of Jill to the Kinetic Energy of John is 1:2 or 1/2. Therefore, the answer is D.

John's Mass Is Half the Mass of Jill