Question

A model rocket is launched with an initial upward velocity 39M/S. The rockets height H (in meters) after t seconds is given by the following. h=39t-5t2Find all values for which the rockets height is 22 meters.

Answer 1

Given:

`h=39t-5t^2`

It is given that h=22m,

`22=39t-5t^2`
`5t^2-39t+22=0`
`t=\frac{39\pm\sqrt[]{39^2-4(5)(22)}}{2(5)}`
`t=\frac{39\pm\sqrt[]{1521-440}}{10}`
`t=\frac{39\pm\sqrt[]{1081}}{10}`
`t=(39\pm32.88)/(10)`
`t=(39+32.88)/(10),(39-32.88)/(10)`
`t=(71.88)/(10),(6.12)/(10)`
`t=7.188,0.612`

The values for the rockets height is 22m are 0.61 seconds and 7.19 seconds.