Answer : option A
[tex]P(t)= -16t^2 -88t +720[/tex]
Top of a tall boulder = 57 foot
To find the time taken for the pebble to hit the boulder
We set p(t) = 57 and solve for t
[tex]57= -16t^2 -88t +720[/tex]
Subtract 57 on both sides
[tex]0= -16t^2 -88t +720-57[/tex]
[tex]0= -16t^2 -88t +663[/tex]
[tex]0= -(16t^2 +88t -663)[/tex]
apply quadratic formula to solve for t
[tex]t= \frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
plug in the values a = 16, b= 88 and c= -663
[tex]t = \frac{-88+-\sqrt{88^2-4(16)(-663)}}{2*16}[/tex]
[tex]t= \frac{-39}{4}[/tex] and [tex]t= \frac{17}{4}[/tex]
t= -9.75 and t = 4.25
Time cannot be negative. So we ignore negative answer
the time taken for the pebble to hit the boulder is 4.25 seconds
