Question

A player runs 100m along the length, and 64m along the width of a football field. What is the magnitude and direction of the player's displacement (indicated by the arrows )?

Answer 1

The player's displacement is approximately 118.7m, and the direction of the displacement is 32.5° from the length of the field towards the width.

Step-by-step explanation:

The magnitude and direction of a player's displacement can be calculated using the Pythagorean theorem and trigonometry, given the player runs 100m along the length and 64m along the width of a football field. The displacement is the vector sum of these two separate movements. First, we find the magnitude of the displacement (S) using:

S = √(length² + width²)

S = √(100m² + 64m²)

S = √(10000 + 4096)

S = √(14096)

S ≈ 118.7m

To find the direction (θ), which is the angle with respect to the length of the field, we use:

θ = tan⁻¹(width/length)

θ = tan⁻¹(64/100)

θ ≈ 32.5°

The direction is measured from the length of the field towards the width, meaning the player's displacement is 118.7m at an angle of 32.5° with respect to the length of the field.