A quarterback takes the ball from the line of scrimmage, runs backward for 8 yards, and then runs sideways parallel to the line of scrimmage for 5 yards. At this point, he throws a 49 yard forward pass straight down the field. What is the magnitude of the football's resultant displacement in yards?

41 yards down the field and 5 yards sideways.

Use the Pythagorean theorem for the hypotenuse. .

43yrds

41 yards

To find the magnitude of the football's resultant displacement, we need to consider the individual displacements made by the quarterback. Let's break it down step by step.

1. The quarterback runs backward for 8 yards. This means he moves 8 yards in the opposite direction from the line of scrimmage. We can represent this as a displacement vector with a magnitude of 8 yards pointing in the negative direction.

2. Next, the quarterback runs sideways parallel to the line of scrimmage for 5 yards. Since he is not moving vertically, this displacement doesn't affect the magnitude of the resultant displacement. We can consider it as a displacement in the x-axis direction.

3. Finally, the quarterback throws a 49 yard forward pass straight down the field. This means he moves 49 yards in the positive direction relative to the line of scrimmage. We can represent this as a displacement vector with a magnitude of 49 yards pointing in the positive direction.

Now, we can find the resultant displacement by adding these vectors together. Since the vertical displacement is opposed by the backward displacement, the magnitude of the resultant displacement can be calculated using the Pythagorean theorem:

Resultant displacement = √((8)^2 + (49)^2)

Calculating this, we get:

Resultant displacement = √(64 + 2401) = √2465 = approximately 49.65 yards

Therefore, the magnitude of the football's resultant displacement is approximately 49.65 yards.