• always use significant figure rules. remember that these rules apply to all numbers that are measurements…

• always use significant figure rules. remember that these rules apply to all numbers that are measurements. during a treasure hunt, cody walks 45.0 m south and 7.50 m to the west. what single straight - line displacement could cody have taken to reach the treasure? (remember that magnitude and angle and direction are all needed for your answer.)

• always use significant figure rules. remember that these rules apply to all numbers that are measurements. during a treasure hunt, cody walks 45.0 m south and 7.50 m to the west. what single straight - line displacement could cody have taken to reach the treasure? (remember that magnitude and angle and direction are all needed for your answer.)

Answer

Explanation:

Step1: Encontrar la magnitud del desplazamiento

Usamos el teorema de Pitágoras. El desplazamiento en el sur es $y = 45.0$ m y el desplazamiento en el oeste es $x = 7.50$ m. La magnitud del desplazamiento $d$ está dada por $d=\sqrt{x^{2}+y^{2}}$. $$d=\sqrt{(7.50)^{2}+(45.0)^{2}}=\sqrt{56.25 + 2025}=\sqrt{2081.25}\approx45.6$ m$$

Step2: Encontrar el ángulo del desplazamiento

Usamos la trigonometría. $\tan\theta=\frac{y}{x}$, donde $\theta$ es el ángulo medido desde el oeste hacia el sur. $$\tan\theta=\frac{45.0}{7.50}=6$$ $$\theta=\arctan(6)\approx80.5^{\circ}$$ El dirección es $80.5^{\circ}$ sur de oeste.

Answer:

Magnitud: $45.6$ m, Ángulo: $80.5^{\circ}$, Dirección: Sur de oeste