A car goes through a curve with a constant velocity of 60mph and experiances a centripital acceleration of 77.4 ft/secsquared. Find the radius of the curve.
centripetal acceleration = v^2/r
be sure to either have all the measurements in either miles and hours OR ft and sec!
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To find the radius of the curve, we can use the formula for centripetal acceleration:
a = v^2 / r
Where:
a = centripetal acceleration
v = velocity
r = radius
First, let's convert the velocity from mph to ft/sec:
60 mph = (60 * 5280 ft) / (60 * 60 sec)
= 88 ft/sec
We are given that the centripetal acceleration is 77.4 ft/sec^2.
Now we can rearrange the formula to solve for radius (r):
r = v^2 / a
Plugging in the values:
r = (88 ft/sec)^2 / (77.4 ft/sec^2)
= 7744 ft^2/sec^2 / 77.4 ft/sec^2
= 100 ft
Therefore, the radius of the curve is 100 ft.