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A railroad track is laid along the arc of a circle of radius 1800. The circular part of the track subtends a central angle 40 degrees. How long in Sec will it take s point on the front of the train moving at 30 mph to go around this portion.
I'm given: Radius-1800 Theta-40 Velocity-30. So, would I use V=r(theta)/time. Then, divide by 60 time to convert to seconds.
Hint: length of arc = 40/360 * pi(2*1800) = pi(3600) / 9 = ?
Still does not really help me out.
Your speed is given in miles per HOUR -- 3600 seconds in a hour.Quote:
Originally Posted by Brndo4u
You can determine the arc length: $\displaystyle 400 \pi$ feet.
(Wilmer gave you that -- I just did the division of 3600 by 9 to leave 400.)
The speed: 30 mph is equivalent to:
$\displaystyle \dfrac{ 30 miles/hour \cdot 5280 feet/mile}{3600 seconds/hour}$ = $\displaystyle \dfrac{44 feet}{second}$
Then divide the arc length by the speed:
$\displaystyle \dfrac{ 400 \pi \, feet }{44 feet / second}$ to get the time in seconds to traverse the arc.
OK; rounding out:
Arc length = 400*pi = 1257 MILES (if the given 1800 is in miles; IS IT?)
1257 / 30 mph = 42 HOURS
42 * 60 * 60 = 151,200 SECONDS.
In other words, your problem makes little sense.
Are you sure you entered it correctly?
