Question

Question #a5e49

Answer 1

a. `20` `m`.
b. `2.06` `s`.

Explanation:

To find the height you only have to substitute `t` in the equation for the number of seconds you what to know its possition,
`d(t)=-16·1^2+30·1+6=20` `m`

and to find the time it took the hat to hit the ground you need to think a bit. If the hat is in the ground it means that de height is `0`, so you can equal the equation to `0` and find the value of `t`.
`-16t^2+30t+6=0`

we can use the formula for quadratics equations.
`t=(-b+-sqrt(b^2-4ac))/(2a)=(-30+-sqrt(30^2-4·(-16)·6))/(2·(-16))=`
`=(-30+-sqrt(900+384))/(-32)=(-30+-sqrt(1284))/(-32)`

`cancel(t_1=(-30+sqrt(1284))/(-32)=-0.18s)`
This solution is not possible because time can't be negative.

`t_2=(-30-sqrt(1284))/(-32)=2.06` `s`