A quarterback takes the ball from the line of scrimmage, runs backwards for 9.0 yards, then runs sideways parallel to the line of scrimmage for 17.0 yards. At this point, he throws a 46.0-yard forward pass straight downfield, perpendicular to the line of scrimmage. What is the magnitude of the football's resultant displacement?

yd

D = -9 + 17i + 46 = 37 + 17i.

X = 37yds, Y = 17 yds.

D = Sqrt(X^2 + Y^2)

To find the magnitude of the football's resultant displacement, we need to determine the straight-line distance between the starting point and the final position after all the movements.

Let's break down the movements of the quarterback:

1. Backwards movement: The quarterback runs backwards for 9.0 yards. This movement creates a displacement in the opposite direction, which we need to subtract from the total displacement.

2. Sideways movement: After running backwards, the quarterback then runs sideways parallel to the line of scrimmage for 17.0 yards. Since this movement is perpendicular to the line of scrimmage, it does not affect the displacement in the vertical direction.

3. Forward pass: Once the quarterback reaches this point, he throws a 46.0-yard forward pass straight downfield, perpendicular to the line of scrimmage. This movement adds to the horizontal displacement.

To calculate the magnitude of the resultant displacement, we need to apply the Pythagorean theorem. The resultant displacement is the hypotenuse of a right triangle formed by the backward movement and the forward pass.

Using the Pythagorean theorem:

Resultant displacement = √((Backward displacement)^2 + (Forward pass displacement)^2)

Backward displacement = 9.0 yards
Forward pass displacement = 46.0 yards

Plugging in the values:

Resultant displacement = √((9.0)^2 + (46.0)^2)
Resultant displacement = √(81 + 2116)
Resultant displacement = √2197
Resultant displacement ≈ 46.9 yards (rounded to one decimal place)

Therefore, the magnitude of the football's resultant displacement is approximately 46.9 yards.

To find the magnitude of the football's resultant displacement, we can use the Pythagorean theorem because the quarterback initially moves backwards and then sideways.

The initial backward displacement is 9.0 yards, and the sideways displacement is 17.0 yards.

Using the Pythagorean theorem:

Resultant displacement = √((backwards displacement)^2 + (sideways displacement)^2)

Resultant displacement = √((9.0)^2 + (17.0)^2)

Resultant displacement = √(81.0 + 289.0)

Resultant displacement = √370.0

Resultant displacement ≈ 19.23 yards

Therefore, the magnitude of the football's resultant displacement is approximately 19.23 yards.