Question

If a football player positioned on the scrimmage line runs straight downfield for 26 yards and then cuts to his left for 6.0 yards to receive a pass, what is the football player's total displacement from the scrimmage line? (Use trigonometry to answer, but remember to draw a diagram to help your understanding.) Give both the magnitude and the angle in your answer

Answer 1

displacement is the straight line distance from initial to final position

here first it go to 26 yard then it makes a pass to left for 6 yards

So here it will make a right angle triangle and the displacement will be its hypotenuse

displacement will be given as

$d = \sqrt{26^2 + 6^2}$

$d = 26.68 yards$

so the displacement of the ball is 26.68 yards

now for the direction

$\theta = tan^{-1}\frac{d_2}{d_1}$

so here the direction will be

$\theta = tan^{-1}\frac{6}{26}$

$\theta = 13 degree$

so the displacement is 26.68 yards at an angle of 13 degree from its initial direction of the motion