Answer to Question #111966 in Mechanics | Relativity for M

Question #111966
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.
1
Expert's answer
2020-04-27T10:22:29-0400
"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. 


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