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A. Find the maximum height it can reach and when it will reach its maximum height. 

B.Find when the object hits the ground

C. Write a function that models the height of the object after t seconds

d. Find when the object is above 96 feet.

 Jan 18, 2021
 #1
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+1

x= x0 + vot + 1/2 at2

ht = 64 + 48t - 16.1t2           Max occurs at   t = - b/2a =  -48 / 2(-16.1)

   use the value of t determined above  in the equation to calculate max height

 

also use the equation to calculate when above 96ft like this

  -16.1t^2 +48t + 64 > 96

  -16.1t^2 + 48t -32 >0     use quadratic formula to find t values...there will be two...the time between is when above 96ft

 Jan 18, 2021
 #2
avatar+116126 
+2

The function  we are working with is

 

f(t)  =-16t^2 + 48t  + 64  =   answer C

 

(A )  the  max  height  occurs    at       -48 / (2 -16)  =  -48/ -32  =  1.5  seconds

 

This height   is     -16(1.5)^2  + 48(1.5) + 64   =   100ft

 

(B)  To find when it  hits the  ground

 

-16t^2   + 48t  + 64  =   0        divide through by -16

 

t^2  - 3t  - 4   =  0    factor

 

(t - 4) ( t +1)   = 0

 

The first factor set to  0  gives us a positive time

 

t - 4    =  0  

t = 4 seconds

 

(D)       -16t^2   +  48t  +  64  >   96        subtract  96 from both sides

 

-16t^2  + 48t  - 32  >  0      divide  trough  by  -16, chage the  dirction of the  inequality  sign

 

t^2  - 3t  + 2  <   0       factor

 

(t - 2)( t - 1)  <  0

 

This is  true when   t is between   1  and  2  seconds

 

 

cool cool cool 

 Jan 18, 2021

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