A quarterback takes the ball from the line
of scrimmage, runs backward for 18.0 yards,
then runs sideways parallel to the line of
scrimmage for 16.0 yards. At this point,
he throws a 49.0-yard forward pass straight
down the field.
What is the magnitude of the football’s
resultant displacement?
Answer in units of yards.
D = -18 + 16i + 49 = 31 + 16i =
sqrt(X^2 + Y^2) = sqrt(31^2 + 16^2) =
To find the magnitude of the football's resultant displacement, we need to calculate the distance between the starting point and the endpoint of the football's trajectory.
First, let's break down the movements:
1. The quarterback runs backward for 18.0 yards. This means he is moving in the opposite direction of the line of scrimmage.
2. Then, the quarterback runs sideways parallel to the line of scrimmage for 16.0 yards. This means he is moving perpendicular to the line of scrimmage.
3. Finally, the quarterback throws a forward pass straight down the field for 49.0 yards. This means he is moving in the direction of the line of scrimmage.
We can visualize these movements as a right-angled triangle, with the backward and sideways movements as the two sides of the triangle, and the forward pass as the hypotenuse.
Using the Pythagorean theorem, we can calculate the magnitude of the football's resultant displacement:
Resultant displacement = √(backward^2 + sideways^2 + forward^2)
Plugging in the values:
Resultant displacement = √(18.0^2 + 16.0^2 + 49.0^2)
Resultant displacement = √(324.0 + 256.0 + 2401.0)
Resultant displacement = √(2981.0)
Resultant displacement ≈ 54.6 yards
Therefore, the magnitude of the football's resultant displacement is approximately 54.6 yards.