Question

Suppose a table-tennis ball is hit in such a way that its path can be modeled by h=-4.9t^2+2.07t, where h is the height in meter above the table and t is the time in seconds. Estimate the maximum height reached by the table-tennis ball. Round to the nearest tenth. Show your work.

Answer 1

Answer: 0.2

You can estimate the maximum height by finding where the equation equals zero and taking the average between these two points.

$h(t)=-4.9t^2+2.07t\\h(t)=t(-4.9t+2.07)\\t=0\\-4.9t+2.07=0 > -4.9t=-2.07 > t=\frac{-2.07}{-4.9}=0.4224\\\frac{0.4224-0}{2}=0.2112=0.2$