Answer to Question #111966 in Mechanics | Relativity for M

Question

A Mazda Miata (950 kg) is traveling 70 mph down the highway at 40 degrees S of E and F-150 truck (1700 kg) is merging on the highway traveling 53 mph. The merge lane joins the highway at 33 degrees N of E. Estimate the resultant direction in words the solve for it and resultant speed in this direction. Convert final speed to mph.

Answer 1

$$950(70\cos{40},-70\sin{40})+1700(53\cos{33},53\sin{33})\\=\left(950+1700\right)(v_x,v_y)$$

$$(v_x,v_y)=(47.7,2.39)\ mph$$

$$v=\sqrt{47.7^2+2.39^2}=47.8\ mph$$

Direction:

$$\theta=\arctan{\frac{2.39}{47.7}}=2.87\degree$$

The the resultant direction is 2.87 degrees N of E.