Question #a5e49

1 Answer
Nov 19, 2017

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