The range without lift.

The data is given in degrees, so we first convert all functions to radians.

Input := 

rad[th_]  := t Pi/180;

Next, we decompose velocity into its horizontal Vx and vertical Vy components recalling that the initial speed was 58 m/sec.

Input := 

Vx = 58 Cos[rad[th]];
Vy = 58 Sin[rad[th]] - 9.8 t;

Exploiting the lack of air resistance, the time it takes for the ball to hit the ground is twice as long as the time it takes to hit its maximum height. This occurs when the vertical component of velocity is zero.

Input := 

time = 2 ( t /. Flatten[Solve[Vy == 0, t]] )

Output =

            Pi th
11.8367 Sin[-----]
             180

Finally, since the horizontal component of velocity Vx is a constant (with respect to time t), we can simply multiply it by the travel time to find the horizontal range of the golf ball.

Input := 

RangeNoLift = Vx time

Output =

            Pi th      Pi th
686.531 Cos[-----] Sin[-----]
             180        180

Here's a graph of the range vs. the launch angle for the classical case of no lift.

Input := 

Plot[RangeNoLift, {th, 0, 90},
	AxesLabel -> {"angle [deg]", "range [m]"}]

Output =

-Graphics-