Final answer:
In physics, a golfer's shot requiring projectile motion analysis involves calculating hang time through the vertical motion equation, and maximum vertical and horizontal displacements using kinematic equations and the given initial velocities.
Step-by-step explanation:
The question involves calculating the hang time, as well as horizontal and vertical displacements for a projectile motion scenario in physics. We are given an initial velocity vector v = (19.0 m/s, 26.0 m/s), where the first component is the horizontal velocity (vx) and the second is the vertical velocity (vy). To determine the hang time, the problem can be approached by focusing on the vertical motion and using the kinematic equations of motion under gravity.
To find the time the golf ball stays in the air, we use the equation for vertical motion: vy,final = vy - g*t, where g is the acceleration due to gravity (9.8 m/s2). Since the ball's upward velocity is equal to the downward velocity at ground impact (ignoring air resistance), we can find the time to reach the maximum height, and then double it to get the total hang time, as the ascent and descent times are equal. The maximum height (hmax) can be found using the formula hmax = vy^2 / (2*g). The horizontal displacement (range) is calculated by the horizontal velocity multiplied by the total hang time, using the formula Range = vx * t.