Question

IM USING 20 POINTS FOR THIS PLS HELP AND SHOW WORK

Answer 1

Answer:

the object is in the air on the time interval (0.24 sec, 6.51 sec)

Step-by-step explanation:

The object is 'in the air' for all t such that h> 0.  We need to find the roots of h = -16t^2 + 108t - 25 = 0.  From the graph we see that both t values are positive.  Once we find them, we subtract the smaller t from the larger t, which results in the length of time the object is in the air.

Use the quadratic formula to find the roots of h(t).  The coefficients of t are {-16, 108, -25}, and so the discriminant b^2 - 4ac is

108² - 4(-16)(-25) = 11664 - 1600 = 10064, whose square root is 100.32.

Then the quadratic formula x = (-b ± √[b² - 4ac)/(2a) becomes

      -108 ± 100.32       108 ± 100.32

t = ---------------------- = --------------------- = 3.375 ± 3.135

             2(-16)                      32

or t = 6.51 or t = 0.24  (both times expressed in seconds).

So, again, the object is in the air on the time interval (0.24 sec, 6.51 sec)