Final answer:
To find the distance the receiver must run to catch the ball, we can break down the given information into horizontal and vertical components. Using trigonometry, we can calculate the horizontal and vertical displacements, and then find the total distance using the Pythagorean theorem.
Step-by-step explanation:
To find the distance the receiver must run to catch the ball, we can break down the given information into horizontal and vertical components. Since the ball travels off course to the right, we need to consider the horizontal displacement (from A to C) and the vertical displacement (from B to C).
To find the horizontal distance, we can use the cosine of the angle between the ball's path and the receiver's position. The horizontal displacement can be calculated as:
Horizontal displacement = 63 yd × cos(6°)
Next, to find the vertical distance, we can use the sine of the same angle. The vertical displacement can be calculated as:
Vertical displacement = 63 yd × sin(6°)
Finally, we can find the total distance the receiver must run by using the Pythagorean theorem:
Total distance = √(Horizontal displacement² - Vertical displacement²)
x² = 63² - 55²
x² = 3969 - 3025
x² = 944
x = √944
x ≈ 30.7 yards
Therefore, the receiver must run approximately 31 yards to catch the ball.