Question

Ball a has half the mass and eight times the kinetic energy of ball

b. what is the speed ratio va / vb ?

Answer 1

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

Answer 2

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=(1)/(2)m_b`

`KE_a=8\ KE_b`

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

`KE=(1)/(2)mv^2`

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

So,

`(KE_a)/(KE_b)=(1/2m_av_a^2)/(1/2m_bv_b^2)`

`(8\ KE_b)/(KE_b)=(1/2(1/2m_b)v_a^2)/(1/2m_bv_b^2)`

`16=(v_a^2)/(v_b^2)`

`(v_a)/(v_b)=(4)/(1)`

Hence, this is the required solution.