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themethetion

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Thread moved from the technical math forums to the schoolwork forums

**TL;DR Summary:**Using vector functions how can I find the minimum average velocity (something greater than 11.86m/s) of a ball if the launch angle is unknown and if I have a point that the object must travel through (11.86, 3.47)?

In my assignment, I developed a function for a lob shot (opposition against the net, the player hitting the ball from the back of the court) in tennis where the ball travels over a player's maximum reach (3.47m) and restriction in court length (23.72m). Therefore through points (11.86, 3.47). The function developed was 3.47= (-4.9/(cos^2(x))) + 11.86tan(x). This gave x/theta as imaginary numbers therefore I'm assuming with an average velocity of 11.86m/s (calculated from professionals performing a lob) the height and distance of 11.86mX and 3.47mY cannot be reached. Therefore I want to determine the minimum velocity and its corresponding launch angle that I can use for the tennis ball to travel through this point while landing before 23.72m. But I'm unsure of how to calculate the minimum velocity without a launch angle.