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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 (m/s)

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.