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Motion of a Projectile Thrown from an Elevated Platform

The motion of a projectile is controlled by Newton's first law

Here, the acceleration, a, is given by a combination of the initial force applied to the projectile, which propels it forward and up, and gravity, which propels it down until it hits the ground.

Initial speed


initial height


initial angle


ground level

Initial Values Entered:

determines the subsequent heights.

Range can be obtained by solving this equation for x with h(x) = 0.

The maximum height attained is most simply obtained by using the kinematic formula:

And we might want to graph the overall trajectory:

Look at the change in the shape of the trajectory, the maximum range, R (how far the projectile goes) and the maximum height, hmax (the height at the top of the parabolic trajectory) as you change the input variables.