A quarterback takes the ball from the line of scrimmage, runs backward for 10 yards, and then runs sideways parallel to the line of scrimmage for 4 yards. At this point, he throws a 32 yard forward pass straight down the field. What is the magnitude of the football's resultant displacement?
26
To find the magnitude of the football's resultant displacement, we need to determine the total distance covered by the quarterback.
First, let's break down the quarterback's movements:
1. He runs backward for 10 yards.
2. Then, he runs sideways parallel to the line of scrimmage for 4 yards.
3. Finally, he throws a 32-yard forward pass straight down the field.
To calculate the magnitude of the resultant displacement, we can use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the backward run, sideways run, and forward pass form a right triangle. The backward run and the sideways run are the two sides, and the resultant displacement is the hypotenuse.
Using the Pythagorean theorem, the magnitude of the resultant displacement can be calculated as follows:
Resultant displacement = √(backward^2 + sideways^2)
Let's plug in the values:
Resultant displacement = √(10^2 + 4^2)
= √(100 + 16)
= √116
≈ 10.77 yards
Therefore, the magnitude of the football's resultant displacement is approximately 10.77 yards.