Question

f 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

In the problem you are given what basically amounts to two sides (the legs) of a right triangle.
We are trying to find the hypotenuse of the triangle (which is the displacement).
Using the Pythagorean Theorem
a^2+b^2=c^2
we will plug in 26 and 6 for a and b, and then solve for c yielding an answer of 26.6833 yards.
To find the angle from the direction he ran forward, we can use a trigonometric function.
I will use the tangent function since we are given the adjacent and opposite sides (tanθ=(opp/.adj.)
tanθ=(6/26).
This yields a theta value of 12.9946 degrees (this is the angle from his initial running direction)