Question

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?

a) 11.9 m
b) 24.5 m
c) 43.1 m
d) 62.5 m

Answer 1

Using the principles of projectile motion and the provided initial speed and angle, the calculations reveal the golfer's ball lands 24.5 m from the green after falling 20 m vertically.

Step-by-step explanation:

The question about the golfer hitting the ball toward the green involves applying the principles of projectile motion in physics. To find out how close the golfer comes to the green, we'll need to calculate the horizontal distance the ball travels before reaching the level of the green, which is 20 m below the fairway. We'll use the angle of projection, the initial velocity, and the vertical displacement in our calculations.

First, we'll find the time it takes for the golf ball to fall 20 m using the vertical motion equation:
h = V_{y0}t + (1/2)gt^2, where h is vertical displacement (20 m), V_{y0} is the initial vertical velocity, t is time, and g is the acceleration due to gravity (9.81 m/s2). We solve for time assuming the initial vertical velocity V_{y0} is the vertical component of the initial velocity.

Then we'll use the horizontal component of the initial velocity and the time calculated to find the horizontal distance using the horizontal motion equation:
x = V_{x0}t, where x is horizontal distance and V_{x0} is the initial horizontal velocity. The initial speed of the ball can be broken down into components using the given angle of 40°.

After solving these equations, we find that the correct answer is b) 24.5 m, meaning the golfer comes within 24.5 m of the green.