A quarterback takes the ball from the line of scrimmage, runs backward for 11.1 yds, then runs sideways parallel to the line of scrimmage for 17.8 yds. At this point, he throws a 52.7 yd forward pass straight downfield, perpendicular to the line of scrimmage. What is the magnitude of the football's resultant displacement?

To find the magnitude of the football's resultant displacement, we can use the Pythagorean theorem.

Step 1: Calculate the horizontal displacement:
The quarterback runs sideways parallel to the line of scrimmage for 17.8 yards, and the football is thrown perpendicular to the line of scrimmage. Therefore, the horizontal displacement is 17.8 yards.

Step 2: Calculate the vertical displacement:
The quarterback runs backward for 11.1 yards, and the football is thrown straight downfield, so there is no vertical displacement.

Step 3: Use the Pythagorean theorem to find the resultant displacement:
The Pythagorean theorem states that the square of the resultant displacement is equal to the sum of the squares of the horizontal and vertical displacements.
Therefore, the resultant displacement (D) can be calculated as:

D^2 = (horizontal displacement)^2 + (vertical displacement)^2

D^2 = 17.8^2 + 0^2

D^2 = 316.84

Taking the square root of both sides, we get:

D = √316.84

D ≈ 17.8

Therefore, the magnitude of the football's resultant displacement is approximately 17.8 yards.

To find the magnitude of the football's resultant displacement, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse (c) of a right triangle is equal to the sum of the squares of the other two sides (a and b).

In this case, we can consider the quarterback's backward run as one side of the triangle, the sideways run as the other side, and the forward pass as the hypotenuse.

Let's calculate step by step:

1. Convert the distances to yards to make sure all values are in the same units.

- The quarterback runs backward for 11.1 yds.
- The quarterback runs sideways for 17.8 yds.
- The quarterback throws a forward pass for 52.7 yds.

2. Square the distances to get the squares of the sides of the triangle.

- Backward run squared = (11.1)^2
- Sideways run squared = (17.8)^2
- Forward pass squared = (52.7)^2

3. Add the squares of the backward and sideways runs to get the sum.

- Sum of squares = (11.1)^2 + (17.8)^2

4. Take the square root of the sum of squares to find the magnitude of the football's resultant displacement.

- Magnitude of resultant displacement = sqrt((11.1)^2 + (17.8)^2)

By evaluating this expression, you can find the magnitude of the football's resultant displacement.