A flatt horizontal road is been designed for 60km/hr speed limit if the maximun acceleration of the car travelling on the road is to be 15m/s at the above speed limit.what is the minimun radius of the curvature of the curve on the road
To find the minimum radius of curvature of the curve on the road, we can use the following formula:
\[a = \frac{{v^2}}{{r}}\]
Where:
a = acceleration (15 m/s^2)
v = velocity/speed (60 km/hr converted to m/s)
r = radius of curvature (unknown)
First, let's convert the speed from km/hr to m/s:
\[60 \text{ km/hr} = \frac{{60 \times 1000}}{{60 \times 60}} \text{ m/s} = 16.67 \text{ m/s}\]
Now we have all the values, and we can rearrange the formula to solve for the minimum radius of curvature:
\[15 \text{ m/s}^2 = \frac{{(16.67 \text{ m/s})^2}}{{r}}\]
Cross multiply to solve for r:
\[15 \times r = (16.67)^2\]
\[r = \frac{{(16.67)^2}}{{15}}\]
Calculating this gives us:
\[r \approx 18.53 \text{ meters}\]
Therefore, the minimum radius of curvature of the curve on the road is approximately 18.53 meters.