Please help i am on a life or death dead line

Question

The height h in feet of the ball kicked into the air can be modeled by h=-16t^2 + 48t, where t is time in seconds. Find the time it takes the ball to reach 36 feet above groun

Answer 1

h=-16t^2+48t

set h=36 and solve for t:

36=-16t^2+48t

0=-16t^2+48t-36  -> subtract 36 from both sides

0=-16(t^2-3t+36/16)  -> factor out a -16

0=t^2-3t+9/4  -> divide both sides by -16

0=(t-3/2)(t-3/2)  -> factor using mental math or plug into quadratic equation

t=3/2 or 1.5 seconds.

 

 

Answer 2

Hi Madison,

 

Since you want to know how long it takes to reach 36 ft. substitute 36 in place of h resulting in 

                                36 = -16t² +48t  Now arrange the equation in standard form.        16t² - 48t + 36 = 0  To simplify the factoring, divide all of the terms by 4 resulting in

                               4t² - 12t + 9  = 0

                           (2t - 3)(2t - 3)  =  0  Set each factor equal to zero and solve for t.    2t - 3 = 0

                             2t = 3

                               t = 1.5 sec.

Answer 3

h = -16² + 48t

36 = -16t² + 48t            substitution

0 = -16t² + 48t - 36       subtract 36 form both sides

0 = 4t² - 12t + 9          divide both sides by -4

0 = (2t - 3)²                  general form

0 = 2t - 3                      zero product rule

3 = 2t                           add 3 to both sides

3/2 = t                          divide both sides by 2

 

At 1.5 seconds the ball is 36 feet off the ground.

Answer 4

Find the vertex using the formula for the x-component for the vertex first:

 

x = -b/2a

x = -48/-32

x = 1.5

 

Plug 1.5 in for x and solve for the y-component of the vertex:

 

h = -16(1.5)² + 48(1.5)

h = 36

 

This confirms that the vertex corresponds to the maximum height of 36 feet, so it takes 1.5 seconds for the ball to reach 36 feet above the ground.