Question

Particle A has half the mass and eight times the kinetic energy of particle B. What is the speed ratio v_A/v_B?

Short answer

Ratio of speed v_A/v_B= 4

Step-by-step solution

Step:1 Given Information

m_a = 1/2m_b

KE_a=8KE_b

Explanation  

First find Kinetic energy

KE_a = 1/2 m_a v_a²...................................(1)

KE_b = 1/2 m_b v_b²...................................(2)

Divide 1 by 2 , we get

$\frac{K{E}_a}{K{E}_b}=\frac{(1/2m_a{v_a}^2)}{(1/2m_b{v_b}^2)}$

As substitute the given ratio m_a = 1/2m_{b and} KE_a=8KE_b

so

$$\begin{gathered} 8=\frac{(1/2m_a{v_a}^2)}{(1/2m_b{v_b}^2)} \\ \frac{{v_a}^2}{{v_b}^2}=8\times 2 \\ \frac{v_a}{v_b}=4 \end{gathered}$$