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Jason jumped off a cliff into the ocean while vacationing with some friends. His height as a function of time could be modeled by the function h(t)= -16t^2 + 16t + 480, where t is the time in seconds and h is the height is feet.
a. How long did it take for Jason to reach his maximum height?
b. What was the highest point that Jason reached?
c. Jason hit the water after how many seconds?

 Mar 10, 2020
 #1
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Jason jumped off a cliff into the ocean while vacationing with some friends. His height as a function of time could be modeled by the function h(t)= -16t^2 + 16t + 480, where t is the time in seconds and h is the height is feet.


a. How long did it take for Jason to reach his maximum height?

The  time  to  reach  the max  height is given by :

-16/ [ 2 * -16]  =  1 / 2  sec


b. What was the highest point that Jason reached?

Highest point  =  -16(1/2)^2  + 16 (1/2) + 480  =  -4 + 8 + 480  =  484  ft

 


c. Jason hit the water after how many seconds?

We need to solve  this :

 

-16t^2 + 16t  + 480  = 0         divide throug  by  - 16

 

t^2  -  t   -  30 =   0      factor

 

(t + 5) ( t - 6)    = 0

 

Seteting each factor to 0  and solving for  t  produces

 

t  =  - 5 sec  [ reject ]

or

t = 6 sec   [ accept ]

 

 

cool cool cool

 Mar 10, 2020

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