A ball is shot out of a cannon at ground level, We know that its height H in feet after t sec given by the function H (t) 144t-16t Com is a. Find H (3), H (6), H (4), and H (5). Why are some of the outputs equal? H (3) feet

H (3) = 288 feet

H (4) = 320 feet

H (5) = 320 feet

H (6) = 288 feet

Step-by-step explanation:

A ball is shot out of a cannon at ground level so the ball will follow a parabolic path.

Since height H and time t of the ball have been described by a function H (t) = 144t - 16t²

Then we have to find the values of H (3), H (4), H (5) and H (6).

H (3) = 144*3 - 16 (3) ²

= 432 - 144

= 288 feet

H (4) = 144*4 - 16 (4) ²

= 576 - 256

= 320 feet

H (5) = 144*5 - 16 (5) ²

= 720 - 400

= 320 feet

H (6) = 144*6 - 16 (6) ²

= 864 - 576

= 288 feet

Here we are getting the value like H (3), H (6) and H (4), H (5) are same because in a parabolic path ball first increase in the height above the ground then after the maximum height it decreases.

Therefore, after t = 3 and t = 6 heights of the canon ball are same. Similarly after t = 4 and t = 5 heights of the canon above the ground are same.