Final answer:
The golf ball will land approximately 74.11 meters from the hole.
Step-by-step explanation:
To determine how far from the hole the golf ball will land, we can analyze the horizontal and vertical components of its motion separately. The initial velocity of the ball is 40.0 m/s at an angle of 50.0 degrees to the horizontal. We can use trigonometry to find the horizontal component of the velocity, which is 40.0 m/s * cos(50.0 degrees) = 25.74 m/s. The time it takes for the ball to reach the ground can be found using the vertical component of its motion. The initial vertical velocity is 40.0 m/s * sin(50.0 degrees) = 30.47 m/s. Using the equation h = vo*t + 0.5*a*t^2, where h is the vertical displacement, vo is the initial velocity, a is the acceleration due to gravity (-9.8 m/s^2), and t is the time, we can solve for t. Plugging in the values, we have 0 = 30.47*t + 0.5*(-9.8)*t^2. This equation is a quadratic equation that can be solved using the quadratic formula. The positive root is the time it takes for the ball to reach the ground, which is approximately 2.88 seconds.
Now that we have the time, we can find the horizontal displacement of the ball using the horizontal component of its velocity and the time. The horizontal displacement is given by d = vo*t, which is 25.74 m/s * 2.88 seconds = 74.11 meters. Therefore, the golf ball will land approximately 74.11 meters from the hole.