This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
This problem involves calculating the design speed for a horizontal curve on a highway, considering superelevation and the coefficient of side friction. Step 1: Identify the given values. Radius of the curve, R = 666.6\, m Rate of superelevation, e = 8\% = (8)/(100) = 0.08 Coefficient of side friction, f = 0.094 Acceleration due to gravity, g = 9.8\, m/s^2 Step 2: State the formula for the design speed on a horizontal curve. The formula that relates speed, radius, superelevation, and friction is: V = sqrt(R g (e + f)) Where V is the speed in meters per second (m/s). Step 3: Substitute the given values into the formula to find the speed in m/s. V = sqrt(666.6\, m) × 9.8\, m/s^2 × (0.08 + 0.094) V = sqrt(666.6 × 9.8 × 0.174) V = sqrt(1137.92412) V ≈ 33.733\, m/s Step 4: Convert the speed from m/s to km/hr. To convert meters per second to kilometers per hour, multiply by (3600)/(1000) or 3.6: V_km/hr = V_m/s × 3.6 V_km/hr = 33.733\, m/s × 3.6\, km/hr per m/s V_km/hr ≈ 121.439\, km/hr The speed is approximately 33.73 m/s or 121.44 km/hr. That's 2 down. 3 left today — send the next one.