Determine the radius of the convex bridge if a car moving at a speed of 72 km / h produces a pressure of 7.5 kN

Determine the radius of the convex bridge if a car moving at a speed of 72 km / h produces a pressure of 7.5 kN at the top point, the weight of the car is 1.5 tons.

Task data: V (speed of a given vehicle) = 72 km / h (in SI V = 20 m / s); P (pressure at the top of the convex bridge) = 7.5 kN (7500 N); m (vehicle weight) = 1.5 t (in SI m = 1500 kg).
Reference values: g (acceleration due to gravity) ≈ 10 m / s2.
We express the radius of the convex bridge from the formula: P = m * (g – an) = m * (g – V2 / R), whence V2 / R = g – P / m and R = V2 / (g – P / m).
Calculation: R = 202 / (10 – 7500/1500) = 80 m.
Answer: The required radius of the convex bridge is 80 m.