Question

Solve the FF problems step by steps

1. A person has a resultant vector of 5.0 m in the Direction 37 degrees North of East. How far north and how far east had he walked?

2. A plane flying due north at 100 meters per second is blown by a strong wind at 500 meters per second due east. What is the plane's resultant velocity?

Answer 1

(1)

$$d_x=dcos\theta=5.0\ m\cdot cos37^{\circ}=4.0\ m\ [E],$$ $$d_y=dsin\theta=5.0\ m\cdot sin37^{\circ}=3.0\ m\ [N].$$

(2) We can find the magnitude of the plane's resultant velocity from the Pythagorean theorem:

$$v_{plane,res}=\sqrt{v_{wind}^2+v_{plane}^2},$$ $$v_{plane,res}=\sqrt{(500\ \dfrac{m}{s})^2+(100\ \dfrac{m}{s})^2}=510\ \dfrac{m}{s}.$$

We can find the direction of the plane's resultant velocity from the geometry:

$$\theta=tan^{-1}(\dfrac{v_y}{v_x})=tan^{-1}(\dfrac{100\ \dfrac{m}{s}}{500\ \dfrac{m}{s}})=11.3^{\circ}\ N\ of\ E.$$