How long is this curve:...?

Question

A curve on a highway subtends an angle of 30 degrees on a circle of radius 2,000 ft.

(a) How long is the curve subtended by this angle?

(b) How long will it take a car traveling 45 mph to round the curve? Show your answer in seconds.

Thanks and good luck!

Answer 1

Why does this sound like a homework problem?
C = Circumfrence (look up the formula and conversion factors).
x = (angle/360deg) * C.
Length: s = C/x.
Time: If C was in feet, convert s to miles first. Next, divide by speed to get hours. Finally, Convert to seconds.

No, I am not going to do your homework for you. But I am pointing you toward how to solve it. Hint: It will be less than 5 minutes.

Answer 2

a) The circumference of a circle is 2πr

But we are only interested in 30/360 or 1/12 of a circle

curve = 1/12 * 2 π 2000 ft
curve = 1047.20 ft

b) (45 m/h * 5280 ft/mi)/3600 sec/hr = 66 ft/sec

so

1047.20 ft / 66 ft/sec = 15.9 sec

Good luck to you, too.

One other suggestion. If you set up your equations to include the units of measurement, you can check your solution approach against how the units cancel.
.

Answer 3

t=s/v=
(2000*Pi*2/12)/(45*5280/3600)=
1047/66=15.86sec

30 degrees is 1/12 of a circumference.
45 mph is 66 fps

(a) 1047 ft
(b) 15.86 sec

Answer 4

s=rTheta = 2000*pi/6 =1047.2 ft
45 mph = 45*5280/60/60 ft/sec
time 15.87 sec