A quarterback takes the ball from the line of scrimmage, runs backward for 19.0 yards, then runs sideways parallel to the line of scrimmage for 12.0 yards. At this point, he throws a 43.0-yard forward pass straight down the field. What is the magnitude of the football’s resultant displacement? Answer in units of yards
Disp. = 43 yds.
To find the magnitude of the football's resultant displacement, we need to calculate the overall distance (magnitude) covered by the quarterback. We can break down the given information into three components: running backward, running sideways, and throwing a forward pass.
1. Backward Run: The quarterback runs backward for 19.0 yards. Since this is a displacement in the opposite direction of the line of scrimmage, we'll consider it as a negative value: -19.0 yards.
2. Sideways Run: The quarterback runs sideways parallel to the line of scrimmage for 12.0 yards. Since this displacement is perpendicular to the line of scrimmage, it does not affect the overall displacement along the field.
3. Forward Pass: The quarterback throws a forward pass straight down the field for 43.0 yards. This displacement is purely in the forward direction.
To find the total displacement, we need to combine the backward run and the forward pass. Since they are in opposite directions, we can subtract the magnitude of the backward run from the magnitude of the forward pass.
Magnitude of the resultant displacement = |43.0 - 19.0|
Calculating this gives us:
Magnitude of the resultant displacement = |24|
Taking the absolute value, the magnitude of the resultant displacement is 24.0 yards.