To find the angle of the curve, you can use the formula:
θ = arctan(V^2 / (R * g))
where:
- θ is the angle of the curve
- V is the velocity of the car in meters per second (m/s)
- R is the radius of the curve in meters (m)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
In this case, the radius of the curve is given as 60 meters and the velocity of the car is given as 70 km/hr.
First, let's convert the velocity from km/hr to m/s.
Using the conversion factor 1 km/hr = 1000 m/3600 s, we can convert 70 km/hr to m/s:
70 km/hr * (1000 m/3600 s) = 19.44 m/s
Now, substitute the values into the formula:
θ = arctan(19.44^2 / (60 * 9.8))
θ = arctan(378.05 / 588)
Using a calculator, find the value of arctan(0.6432) to get the angle of the curve.
θ ≈ 32.49°
Therefore, the angle of the curve is approximately 32.49°.