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I am writing a computer program, and do not remember what the equation to describe a projectile in motion. I need to program the computer so that my basketball player will shoot accurately with respect to gravity. I thought the equation was a parabola, but that does not seem quite right. Can anyone help me?

Yup, it should be a parabola. THe equation for projectile motion is the same for any projectile - you can look it up in any mechanics text, but here it is again anyway:

x(t) = x0 + t v0 + t^2/2 a0

where everything except t is a vector, t is the time, x is position, x0 is initial position, v0 is initial velocity, and a0 is the (constant) acceleration of gravity in the downward direction at 9.8 m/s^2

Arthur Smith

I do not think that is quite what Dave needs. The motions in the horizontal(here denoted by x) and vertical (here denoted by y) directions, as functions of time, are:

x = x0 + V*cos(theta)*t and y = y0 + V*sin(theta)*t - (1/2)*g*t^2

where (x0, y0) is the location of the ball, relative to some arbitrarily chosen origin of coordinates, at time t=0 (the time when the ball leaves the player's hands), V is the speed of the ball at time t=0, theta is the angle that the velocity vector makes with the horizontal at time t=0, and g is the acceleration due to gravity (g = 9.8 m/sec^2 if x and y are in meters, positive y is "up", and t is in seconds.) You *can* solve the x- equation for t and substitute that into the y-equation to show that the path taken by the basketball (ignoring air resistance and other air- related effects) is a parabola. So you could choose x-values, compute the corresponding y-values, and plot these pairs. You could also choose values for t and compute x and y at these different times using the x and y equa- tions above.


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