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Verified Answer :

MissPhiladelphia

This can be solve using the formula of kinetic energy

K = 0.5 Mv^2

Where k is the kinetic energy

M is the mass

V is the velocity

So v = sqrt (2k/M)

Since Ma = 0.5Mb

Ka = 8Kb

So Va/Vb = sqrt(16Kb/0.5Mb) / sqrt(2Kb/Mb)

Va/Vb = 4

Explanation :

It is given that there are two balls a and b. Ball a has half the mass of ball b. The kinetic energy of ball a is eight times the kinetic energy of ball b.

\(m_a=\dfrac{1}{2}m_b\)

\(KE_a=8\ KE_b\)

We know that the kinetic energy of an object is given by :

\(KE=\dfrac{1}{2}mv^2\)

Taking ratios of kinetic energy of both balls a and b.

So,

\(\dfrac{KE_a}{KE_b}=\dfrac{1/2m_av_a^2}{1/2m_bv_b^2}\)

\(\dfrac{8\ KE_b}{KE_b}=\dfrac{1/2(1/2m_b)v_a^2}{1/2m_bv_b^2}\)

\(16=\dfrac{v_a^2}{v_b^2}\)

\(\dfrac{v_a}{v_b}=\dfrac{4}{1}\)

Hence, this is the required solution.                          

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