Golf math ii how does this trajectory relate to the trajecto

Golf math ii. how does this trajectory relate to the trajectory for the drive on the previous hole

Solution

(1) y = 10+0.5x-0.002x²

         = -a(x-b)² +c

Translated and scaled sutiably , the equation looks like

y=-x² , which is a parabola having attaining a (global) maximum , as can be expected as per Physical conditions (projectile)

(2) The points where y=0 (and x positive) correspond to the range.of the projectile.

Rewriting the equation , we obtain

                                x² - 250x- 5000=0

As the discriminant is (250)² + 4x 5000,

This square root may be estimated to be greater than 250 (trivially) , so the root >( 250+250)/2 =250 yards , as required.

A better estimate (from above ) of the discriminant is the square root of (62500+20000) , which we may take to be 300.

With this a lower bound for the distance x would be (250+300)/2= 275 yards.

Using the calculator , the exact value of x =268.614 yards