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Danielle jumped of a ledge into the ocean in Hawaii while vacationing with her family.  Danielle's hight as a fucntion of time is modeled beow.  Where t is the time in second and h is the height in feet.

 

h(t) = -16t^2 + 16t + 96

 

A) How long did it take for Danielle to reach her maximum height? (In seconds)

 

B) What was the highest point that Danielle reached (In feet)

C)After how many seconds did Danielle hit the water?

 Mar 3, 2021
 #1
avatar+570 
+1

A

t=-(16/2$\cdot$(-16))=$\boxed{\frac12}$

 

B

h(t)=-16(1/2)^2+16(1/2)+96=$\boxed{100}$

 

C

h=-16(0)^2+16(0)+96=$\boxed{96}$

 

(not sure about C, I'm kinda bad at functions)

 Mar 3, 2021
 #2
avatar+34397 
+2

First two are good SW...but do you think 96 seconds sounds like an appropo amount of time before she hits the water ??

 

When D hits the water her height = 0

 

0 = - 16t^2 + 16t + 96     use Quadratic formula or factoring to find the POSITIVE value of 't

                     a = -16      b = 16    c = 96

 

\(t = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

 Mar 3, 2021
 #3
avatar+570 
0

Ooooh, thank you :) (I thought you should substitute t as 0 instead of the function :/)

SparklingWater2  Mar 3, 2021

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