Question

Clay Matthews, a linebacker for the Green Bay Packers, can reach a speed of 10.0 m/s. At the start of a play, Matthews runs downfield at 45° with respect to the 50-yard line and covers 8.0 m in 1 s. He then runs straight down the field at 90° with respect to the 50-yard line for 12 m, with an elapsed time of 1.2 s. (a) What is Matthews’ final displacement from the start of the play? (b) What is his average velocity?

a) (i) 13.5 m, 15.0 m
(ii) 15.0 m, 12.0 m
(iii) 13.5 m, 12.0 m
(iv) 12.0 m, 13.5 m

b) (i) 6.7 m/s
(ii) 7.0 m/s
(iii) 5.0 m/s
(iv) 6.0 m/s

Answer 1

Clay Matthews' final displacement from the start of the play can be calculated by vector addition of the two parts of his run. His average velocity is calculated by dividing the total displacement by the total time of his movements. By solving these, we can find the requested measurements.

Step-by-step explanation:

The problem involves calculating linebacker Clay Matthews' movement on the football field in terms of displacement and average velocity. Displacement is a vector quantity representing the change in position of an object. It requires both magnitude and direction. The average velocity is a ratio of the total displacement to the total time taken.

For part (a), we calculate the final displacement using the provided distances and angles. Running at 45° with respect to the 50-yard line for 8.0 m constitutes the first part of the displacement, and running straight down the field at 90° for 12 m constitutes the second part of the displacement. By breaking these movements into components and using vector addition, we can find the total displacement.

For part (b), we calculate the average velocity by dividing the total displacement by the total time it took for Matthews to cover the displacement. This includes the time for the first and second part of his run.