Question

A ball is thrown from an initial height of 2 meters with an initial upward velocity of 15 m/s. The balls height h (in meters) after t seconds is given by the following:h=2+15t-5t^2Find all values of t doe which the balls height is 7 meters. Round your answer to the nearest hundredth.

Answer 1

Given:

`h=2+15t-5t^2`

Let the height of the ball is 7 meteres.

h=7,

`7=2+15t-5t^2`
`5t^2-15t-2+7=0`
`5t^2-15t+5=0`
`t^2-3t+1=0`
`t=\frac{3\pm\sqrt[]{3^2-4(1)(1)}}{2(1)}`
`t=\frac{3\pm\sqrt[]{9-4}}{2}`
`t=\frac{3\pm\sqrt[]{5}}{2}`
`t=\frac{3+\sqrt[]{5}}{2},\frac{3-\sqrt[]{5}}{2}`
`t=(3+2.24)/(2),(3-2.24)/(2)`
`t=(5.24)/(2),(0.76)/(2)`
`t=2.62,0.38`

The ball in the height of 7 meters at 0.38 seconds and 2.62 seconds.