In real life as opposed to an idealized textbook problem, during the approximate parabolic flight of the ball, gravity will act straight down and is constant. Air resistance will act in the opposite direction to the velocity and will vary with velocity (faster —> more, slower —> less but the actual equation can be quite complicated often related to higher powers of the velocity than v^1). The force will be the vector sum of Fg and Fa. Add spin and Bernoulli’s forces come into play. With backspin, there will be less air pressure under neath the ball than on top of the ball giving a slight upward force which reduces the effect of gravity slightly – but remember, spin will be slowing down.Can you see why without idealizations and approximations, the vast majority of significant problems in physics and engineering cannot be solved. The best solution for a golfer, Practice, Practice, Practice !!Because computer can quickly calculate iterations and successive approximations, we can land the Curiosity rover on Mars. GO Physics !! GO Math !!
With a BS & MS in physics and a career in physics, I not only learned to think in radians and the metric system, once I started programming in machine language using an Assembler, I learned to think and do arithmetic in hexadecimal — base 16. I can do calculations in base 2 (1’ & 0’s) or any base if I take my time. FULL DISCLOSURE: Now that I’ve been retired for 14 yrs and do a lot of sailing with a magnetic compass and a GPS, I’ve reverted to thinking in English units, degrees, knots, and nautical miles. If you don’t use it, you lose it. That’s what my wife keeps telling me.
In real life as opposed to an idealized textbook problem, during the approximate parabolic flight of the ball, gravity will act straight down and is constant. Air resistance will act in the opposite direction to the velocity and will vary with velocity (faster —> more, slower —> less but the actual equation can be quite complicated often related to higher powers of the velocity than v^1). The force will be the vector sum of Fg and Fa. Add spin and Bernoulli’s forces come into play. With backspin, there will be less air pressure under neath the ball than on top of the ball giving a slight upward force which reduces the effect of gravity slightly – but remember, spin will be slowing down.Can you see why without idealizations and approximations, the vast majority of significant problems in physics and engineering cannot be solved. The best solution for a golfer, Practice, Practice, Practice !!Because computer can quickly calculate iterations and successive approximations, we can land the Curiosity rover on Mars. GO Physics !! GO Math !!