Question

vector addition quiz l - mu
if an airplane is flying 100 mph south but there is a crosswind pushing the airplane 35 mph to the west, then what would the resulting velocity be?
○ 11.4 mph, sw
○ 11,225 mph, ne
○ 105.9 mph, sw
○ 104.4 mph, ne

Explanation:

Step1: Identify velocity vectors

Let $\vec{v}_p = 100$ mph South, $\vec{v}_w = 35$ mph West. These are perpendicular vectors.

Step2: Calculate resultant speed

Use Pythagorean theorem:
$$v = \sqrt{v_p^2 + v_w^2}$$
$$v = \sqrt{100^2 + 35^2} = \sqrt{10000 + 1225} = \sqrt{11225} \approx 105.9$$

Step3: Determine direction

Since the plane moves South and wind pushes West, the direction is Southwest (SW).

Answer:

105.9 mph, SW