Question

A 5.0-kg body has three times the kinetic energy of an 8.0-kg body. Calculate the ratio of the speeds of these bodies.

a) 3:2
b) 2:1
c) 5:3
d) 1:3

Answer 1

To calculate the ratio of the speeds of the two bodies, you can use the equation for kinetic energy. Since the 5.0-kg body has three times the kinetic energy of the 8.0-kg body, you can set up an equation and solve for the ratio of the speeds.

Step-by-step explanation:

To calculate the ratio of the speeds of the two bodies, we can use the equation for kinetic energy:

Kinetic energy = 0.5 * mass * velocity^2

Given that the 5.0-kg body has three times the kinetic energy of the 8.0-kg body, we can set up the equation:

0.5 * 5.0 * v1^2 = 3 * 0.5 * 8.0 * v2^2

Simplifying, we get:

v1^2 = 24 * v2^2

Taking the square root of both sides, we have:

v1 = 2 * sqrt(6) * v2

Therefore, the ratio of the speeds is 2:√6, which is approximately 2:2.45.