Question

A ball is thrown from an initial height of 3 meters with an initial upward velocity of 25 m/s. The ball's height h (In meters) after t seconds is given by thefollowingh = 3 + 25t-512Find all values of t for which the ball's height is 13 meters.Round your answer(s) to the nearest hundredth.(If there is more than one answer, use the "or" button.)

Answer 1

The ball's height h after t seconds is defined by

`h(t)=3+25t-5t^2`

To find the velues of t for which the balls height is 13 m.

`\begin{gathered} h(t)=13 \\ 3+25t-5t^2=13 \\ 5t^2-25t+10=0 \\ t^2-5t+2=0 \\ t=\frac{5\pm\sqrt[]{17}}{2} \\ t=4.562,0.438 \\ =4.56,\text{ 0.44} \end{gathered}`

So, after 0.44 seconds and 4.56 seconds (Rounding off to the nearest hundredth), the height of the ball is 13 m.