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 players 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.

27 yd and 13° to the left of the scrimmage line

27 yd and 14° to the left of the scrimmage line

33 yd and 13° to the left of the scrimmage line

33 yd and 14° to the left of the scrimmage line

Explanation:

Step1: Aplicar teorema de Pitágoras

El movimiento del jugador forma un triángulo rectángulo. Las dos distancias son los catetos. La magnitud de la desplazamiento $d$ se encuentra con $d=\sqrt{a^{2}+b^{2}}$, donde $a = 26$ yardas y $b=6$ yardas. Entonces $d=\sqrt{26^{2}+6^{2}}=\sqrt{676 + 36}=\sqrt{712}\approx 26.7\approx27$ yardas.

Step2: Calcular el ángulo

Usamos la tangente. $\tan\theta=\frac{b}{a}$, donde $a = 26$ yardas y $b = 6$ yardas. Entonces $\tan\theta=\frac{6}{26}\approx0.2308$. $\theta=\arctan(0.2308)\approx13^{\circ}$.

Answer:

27 yd and 13° to the left of the scrimmage line