Question

A body with a mass of 5 Kg has the same kinetic energy as a second body. The second body has a mass of 10 kg and is moving at a speed of 20 m/s. How fast is the second body moving?

Answer 1

First body:

$E_{k_1}=\frac{1}{2}.m.v^2\\ \\ E_{k_1}=\frac{1}{2}.5.v_1^2=\frac{5}{2}.v_1^2$

Second body:

$E_{k_2}=\frac{1}{2}.m.v_2^2\\ \\ E_{k_2}=\frac{1}{2}.10.(20)^2=2.000 \ J$

From description of the task we have:

$E_{k_1}=E_{k_2}\\ \\ \frac{5}{2}.v_1^2=2.000 \ J\\ \\ 5.v_1^2=4.000 \ J\\ \\ v_{1}^2=800 \ J\\ \\ v_{1}= \sqrt{800} \ J \approx 28,3 \ m/s$