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

54 A ball is to be shot from level ground with a certain speed. Figure 4-36 shows the range \( R \) it will have versus the launch angle \( \theta_0 \). The value of \( \theta_0 \) determines the flight time; let \( t_{max} \) 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 \( 0.500 t_{max} \)?