Halliday, Resnick & Walker — Motion in Two and Three Dimensions: Problem 54

A ball is to be shot from level ground with a certain speed. Figure 4.25 shows the range \(R\) it will have versus the launch angle \(\theta_0\). The value of \(\theta_0\) determines the flight time; let \(t_{\text{max}}\) represent the maximum flight time. What is the least speed the ball will have during its flight if \(\theta_0\) is chosen such that the flight time is \(0.500 t_{\text{max}}\)?