d. Find omega in degrees per second if r = 2.5 feet and v = -10 feet per minute,

Question

d. Find omega in degrees per second if r = 2.5 feet and v = -10 feet per minute, e. The center line of a freeway curve is laid out as an arc of a circle of radius 300 meters. What is the length of the center line of the curve if it subtends an angle of 20 degree at the center of the circle? f. Find the linear velocity, in centimeters per minute, of the tip of an hour hand of a clock, if the hour hand has a length of 1.5 decimeters. g. Prove that the area A of the sector of a circle as shown in the figure below with a central angle theta is given by A = 1/2 r^2 m^R (theta) (a) 3.62 meters per second; (b) 3.000 radians per minute; (c) -54 pi decimeters per second d) -12/pi or -3.82 degrees per second; (e) 104.72 meters; (f) 0.13 centimeters per minute (g) The area of the circle A = pi r^2 pi r^2/2 pi^R = A/m^R(theta) rightarrow (2 pi^R)(A) = (pi r^2)[m^R(theta)] A = 1/2 r^2 m^R (theta)QED

Explanation / Answer

d) r=2.5ft , v=-10 ft per min = -10/60 ft per sec

w=v/r

w=( -10/60)/2.5

w=( -1/15) radians per second

w=( -1/15)*(180/) degrees per second

w=( -12/) degrees per second

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e)length of arc =ro*(/180o)

length of arc =300*20*(/180)

length of arc =104.72

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f)length of hour hand r=1.5 decimeters =15 centimeters

angular velocity w=360 degrees per hour

w=5o per min

w=5o(/180o) =(/36) rad per min

linear velocity v =rw

linear velocity v =15*(/36)

linear velocity v =1.3 centimeter per minute

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9)area of sector =(1/2)r2    when is in radians

i donnot know what mR() represents

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