Vector a Overscript right-arrow EndScripts has a magnitude of 5.20 m and is directed east. Vector b Overscript right-arrow EndScripts has a magnitude of 3.70 m and is directed 36.0° west of north. What are (a) the magnitude and (b) the direction (counterclockwise from east) of a Overscript right-arrow EndScripts plus b Overscript right-arrow EndScripts? What are (c) the magnitude and (d) the direction (counterclockwise from east) of b Overscript right-arrow EndScripts minus a Overscript right-arrow EndScripts?
3 answers
33. An automobile tire is rated to last for 50,000 miles. Estimate the number o revolutions the tire will make in its lifetime.
36o W. of N. = 90+36 = 126o CCW from E.
(a+b) = 5.2 + 3.70[126o].
(a+b) = 5.2 + 3.70*Cos126+3.70*sin126,
(a+b) = 5.2 - 2.17+2.99i,
(a+b) = 3.03 + 2.99i = 4.26m[44.62o]
A. Magnitude = 4.26 m.
B. Direction = 44.62o.
(b-a) = 3.70[126o] - 5.2.
(b-a) = -2.17+2.99i - 5.2,
(b-a) = -7.37 + 2.99i = 7.95m[-22.08] = 7.95m[158o].
C. Magnitude = 7.95 m.
D. Direction = 158o.
(a+b) = 5.2 + 3.70[126o].
(a+b) = 5.2 + 3.70*Cos126+3.70*sin126,
(a+b) = 5.2 - 2.17+2.99i,
(a+b) = 3.03 + 2.99i = 4.26m[44.62o]
A. Magnitude = 4.26 m.
B. Direction = 44.62o.
(b-a) = 3.70[126o] - 5.2.
(b-a) = -2.17+2.99i - 5.2,
(b-a) = -7.37 + 2.99i = 7.95m[-22.08] = 7.95m[158o].
C. Magnitude = 7.95 m.
D. Direction = 158o.
C = pi * Diameter = Circumference.
We need to know the radius or diameter of the tire.
Rev. = d/C.
d = 50,000 Miles.
d and C must be in the same unit(meters or miles).
We need to know the radius or diameter of the tire.
Rev. = d/C.
d = 50,000 Miles.
d and C must be in the same unit(meters or miles).
16 answers