Answer :
Answer: The required fraction = [tex]\dfrac18[/tex]
Step-by-step explanation:
Let the required fraction = [tex]\dfrac{p}{q}[/tex]
Given: Initial height = 192 inches
Height of ball after second bounce = [tex]\dfrac{p}{q}\times192[/tex]
Height of ball after third bounce = [tex]\dfrac{p}{q}\times\dfrac{p}{q}\times192=192\dfrac{p^2}{q^2}[/tex]
After the third bounce it is 3 inches off the ground.
So,
[tex](\dfrac{p}{q})^2192=3\\\\\\(\dfrac{p}{q})^2=\dfrac{3}{192}\\\\(\dfrac{p}{q})^2=\dfrac{1}{64}\\\\(\dfrac{p}{q})^2=(\dfrac{1}{8})^2\\\\ \dfrac{p}{q}=\dfrac{1}{8}[/tex]
Hence, The required fraction = [tex]\dfrac18[/tex]