You are trying out for the position of place-kicker on a professional football team. With the ball teed 50.0 m from the goalposts with a crossbar 3.05 m off the ground, you kick the ball at 28 m/s and 31° above the horizontal.

(a) Is the field goal attempt good?

(b) By how much is it under or over the bar?

(c) How far behind the plane of the goalposts does the ball land?

To determine whether the field goal attempt is good, we need to analyze the trajectory of the ball and see if it passes through the goalposts.

(a) To start off, let's separate the initial velocity of the ball into its horizontal and vertical components. The vertical component can be found by multiplying the initial velocity (28 m/s) by the sine of the angle of 31°:

Vertical component = 28 m/s * sin(31°)

Next, we need to calculate the time it takes for the ball to reach its highest point. The vertical motion of the ball follows a projectile motion, which we can analyze using the following kinematic equation:

Vertical displacement = (Vertical component)^2 / (2 * g)

Where "g" is the acceleration due to gravity (approximately 9.8 m/s^2). In this case, the vertical displacement is the height of the crossbar (3.05 m). We can rearrange the equation to solve for time:

Time to reach the highest point = square root((2 * vertical displacement) / g)

Once we have the time, we can calculate the horizontal displacement using the equation:

Horizontal displacement = horizontal component * time

The horizontal displacement is the distance behind the plane of the goalposts where the ball lands (c). To determine whether the field goal is good (yes/no), we need to check if the horizontal displacement is within the width of the goalposts (50.0 m).

(b) If the field goal attempt is not good, we can calculate by how much it is under or over the bar by subtracting the height of the crossbar from the vertical displacement.

Now, let's calculate all the required values and determine the answers to the questions.