Question

Two objects, C & D, have the same momentum. Object C has ½ the mass of object D. Find the value of the ratio of velocity C to velocity D.
Part 2
Find the value of the ratio of kinetic energy C to kinetic energy D. 

Answer 1

These are two questions and two answers.

Part 1. Fin the value of the ration of velocity C to velocity D.

Answer: 2

Explanation:

1) Formula: momentum = mass * velocity

2) momentum C = mass C * velocity C

3) momentum D = mass D * velocity D.

4) C and D have the same momentum =>

mass C * velocity C = mass D * velocity D

5) mass C = (1/2) mass D => mass C / mass C = 1/2

6) use in the equation stated in the point 4)

velocit C / velocity D = mass D / mass C

using the equation stated in point 5:

mass D / mass C = 1 / [ mass C / mass D] = 1 / [1/2] = 2

=>

7) velocity C / velocity D = mass D / mass C = 2

Part 2: ratio of kinetic energy C to kinetic energy D.

Answer: 2

Explanation:

1) formula: kinetic energy KE = (1/2) mass * (velocity)^2

2) KE C = (1/2) mass C * (velocity C)^2

3) KE D = (1/2) mass D * (velocity D)^2

4) KE C / KE D =

(1/2) mass C * (velocity C)^2        mass C        (velocity C)^2
--------------------------------------- = --------------- * ---------------------- = (1/2) * (2)^2
(1/2) mass D *( velocity D)^2        mass D        v(velocity D)^2

= 4 / 2 = 2