Guide for non-golfers: the tee is where the bal is launched from, and the green

a) The ball is 5.58 s in the air.

b)  The horizontal distance from the tee to the hole is 197 m.

Explanation:

The vector that describes the position of the ball at time t can be calculated as follows:

r = (x0 + v0 · t · cos α, y0 + v0 · t · sin α + 1/2 · g · t²)

Where:

x0: initial horizontal position

v0: initial velocity

t: time

α:  launching angle

y0: initial vertical position

g: acceleration due to gravity  (-9.80 m/s² considering the upward direction as positive)

Please, see the figure for a description of the situation. Notice that the frame of reference is located at the throwing point.

a) We know that at final time the vertical position of the ball is -18 m relative to the launching point (see figure). Then, using the equation for the y-component of the vector r, we can obtain the time of flight:

y = y0 + v0 · t · sin α + 1/2 · g · t²

-18.0 m = 0 m + 42.0 m/s · t · sin 35° - 1/2 · 9.8 m/s² · t²

0 = -4.9 · m/s² · t² + 42.0 m/s · t · sin 35° + 18.0 m

Solving the quadratic equation:

t = 5.58 s  

b) The horizontal distance traveled by the ball is given by the x-component (rx in the figure) of the vector r at final time. Then:

x = x0 + v0 · t · cos α

x = 0 m + 42.0m/s · 5.58 s · cos 35° = 192 m

Since the ball lands at 5 m of the hole, the horizontal distance from the tee to the hole is (192 m + 5.00 m) 197 m.