Little-known fact The shortest day of the year occurs on the winter solstice (near December 21) and the longest day of the year occurs on the summer solstice (near June 21). However, the latest sunrise and the earliest sunset do not occur on the winter solstice, and the earliest sunrise and the latest sunset do not occur on the summer solstice. At latitude 40° north, the latest sunrise occurs on January 4 at 7:25 A.M. (14 days after the solstice), and the earliest sunset occurs on December 7 at 4:37 P.M. (14 days before the solstice). Similarly, the earliest sunrise occurs on July 2 at 4:30 A.M. (14 days after the solstice) and the latest sunset occurs on June 7 at 7:32 P.M. (14 days before the solstice). Using sine functions, devise a function s ( t ) that gives the time of sunrise t days after January 1 and a function S ( t ) that gives the time of sunset t days after January 1. Assume that s and S are measured in minutes and s = 0 and S = 0 correspond to 4:00 A.M. Graph the functions. Then graph the length of the day function D ( t ) = S ( t ) − s ( t ) and show that the longest and shortest days occur on the solstices.
Little-known fact The shortest day of the year occurs on the winter solstice (near December 21) and the longest day of the year occurs on the summer solstice (near June 21). However, the latest sunrise and the earliest sunset do not occur on the winter solstice, and the earliest sunrise and the latest sunset do not occur on the summer solstice. At latitude 40° north, the latest sunrise occurs on January 4 at 7:25 A.M. (14 days after the solstice), and the earliest sunset occurs on December 7 at 4:37 P.M. (14 days before the solstice). Similarly, the earliest sunrise occurs on July 2 at 4:30 A.M. (14 days after the solstice) and the latest sunset occurs on June 7 at 7:32 P.M. (14 days before the solstice). Using sine functions, devise a function s ( t ) that gives the time of sunrise t days after January 1 and a function S ( t ) that gives the time of sunset t days after January 1. Assume that s and S are measured in minutes and s = 0 and S = 0 correspond to 4:00 A.M. Graph the functions. Then graph the length of the day function D ( t ) = S ( t ) − s ( t ) and show that the longest and shortest days occur on the solstices.
Solution Summary: The author calculates the length of the day function and shows that the longest and shortest days occur on the solstices.
Little-known fact The shortest day of the year occurs on the winter solstice (near December 21) and the longest day of the year occurs on the summer solstice (near June 21). However, the latest sunrise and the earliest sunset do not occur on the winter solstice, and the earliest sunrise and the latest sunset do not occur on the summer solstice. At latitude 40° north, the latest sunrise occurs on January 4 at 7:25 A.M. (14 days after the solstice), and the earliest sunset occurs on December 7 at 4:37 P.M. (14 days before the solstice). Similarly, the earliest sunrise occurs on July 2 at 4:30 A.M. (14 days after the solstice) and the latest sunset occurs on June 7 at 7:32 P.M. (14 days before the solstice). Using sine functions, devise a function s(t) that gives the time of sunrise t days after January 1 and a function S(t) that gives the time of sunset t days after January 1. Assume that s and S are measured in minutes and s = 0 and S = 0 correspond to 4:00 A.M. Graph the functions. Then graph the length of the day function D(t) = S(t) − s(t) and show that the longest and shortest days occur on the solstices.
What are the correct answers for the second and third question on this page. I am on the Cartesian vectors unit in calculu
Trolley of the overhead crane moves along the bridge rail. The trolley position is
measured from the center of the bridge rail (x = 0) is given by x(t) = 0.5t^3-6t^2+19.5t-14 : 0 <= t <= 3 min. The
trolley moves from point A to B in the forward direction, B to C in the reverse direction and C to D again in the
forward direction.
CONTROL PANEL
END TRUCK-
RUNWAY BEAM-
BRIDGE RAIL
HOIST
-TROLLEY
TROLLEY BUMPER
TROLLEY DRIVE
LPENDANT TRACK
-TROLLEY CONDUCTOR
TRACK
WIRE ROPE
-HOOK BLOCK
-BRIDGE DRIVE
-END TRUCK BUMPER
-RUNWAY RAIL
TROLLEY END STOP
-CONDUCTOR BAR
PENDANT FESTOONING
TROLLEY FESTOONING
PENDANT CABLE
PENDANT
x(t)=0.5t^3-6t^2+19.5t-14
v(t)=1.5t^2-12t+19.5
a(t)=(dv(t))/dt=3t-12
Fig. T2.2: The overhead crane
Total masses of the trolley, hook block, and the load attached to the hook block are 110 kg, 20
kg, and 150 kg. Damping coefficient, D, is 40 kg/s.
What is the total amount of energy required from the trolley motor to move the system
[Hint: Use Newton's 2nd law to obtain the…
CONTROL PANEL-
BRIDGE RAIL
HOIST
-TROLLEY
TROLLEY BUMPER
-BRIDGE DRIVE
END TRUCK-
RUNWAY BEAM-
END TRUCK BUMPER
-RUNWAY RAIL
TROLLEY DRIVE
TROLLEY END STOP
-CONDUCTOR BAR
LPENDANT TRACK
TROLLEY CONDUCTOR
TRACK
-WIRE ROPE
PENDANT FESTOONING
TROLLEY FESTOONING
-PENDANT CABLE
-HOOK BLOCK
PENDANT
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