Freefall In the absence of frictional drag, an object near the surface of the earth will fall with the constant acceleration of gravity g. Position and speed at any time can be calculated from the motion equations. Illustrated here is the situation where an object is released from rest. It's position and speed can be predicted for any time after that. Since all the quantities are directed downward, that direction is chosen as the positive direction in this case. At time t = s after being dropped, the speed is vy = m/s = ft/s , The distance from the starting point will be y = m= ft Enter data in any box and click outside the box.

Note that you can enter a distance (height) and click outside the box to calculate the freefall time and impact velocity in the absence of air friction. But the calculation assumes that the gravity acceleration is the surface value g = 9.8 m/s², so the height is great enough for gravity to have changed significantly the results will be incorrect.

Horizontal Launch

All the parameters of a horizontal launch can be calculated with the motion equations, assuming a downward acceleration of gravity of 9.8 m/s².

Time of flight t = s Vertical impact velocity vy = m/s Launch velocity v0 = m/s Height of launch h = m Horizontal range R = m Calculation is initiated by clicking on the formula in the illustration for the quantity you wish to calculate.

General Ballistic Trajectory

Will it clear the fence?

The basic motion equations can be solved simultaneously to express y in terms of x.

For launch velocity v0 = m/s = ft/s, launch angle θ = degrees, and horizontal range x = m = ft, the calculated height is y = m = ft. The time of flight is t = s.

Where will it land?

Where will it land?

The basic motion equations give the position components x and y in terms of the time. Solving for the horizontal distance in terms of the height y is useful for calculating ranges in situations where the launch point is not at the same level as the landing point.

Launch velocity v0 = m/s = ft/s, launch angle θ = degrees, and trajectory height y = m = ft,

The two calculated times are t1 = s and t2 = s. The corresponding ranges are x1 = m =ft and x2 = m =ft.

Note that the value y in the illustration is downward and it is presumed that upward is positive. To reproduce the scenario in the diagram, the input value of y should be negative.

Launch Velocity

The launch velocity of a projectile can be calculated from the range if the angle of launch is known. It can also be calculated if the maximum height and range are known, because the angle can be determined.

From the range relationship, the launch velocity can be calculated. For range R = m = ft, and launch angle θ = degrees, the launch velocity is v0 = m/s = ft/s.

Launch Velocity

The launch velocity of a projectile can be calculated from the range if the angle of launch is known. It can also be calculated if the maximum height and range are known, because the angle can be determined.

For range
R = m = ft,
and peak height
h = m = ft,

the launch velocity is
v₀m/s = ft/s.

The required launch angle is
θ = degrees.

Angle of Launch

Variation of the launch angle of a projectile will change the range. If the launch velocity is known, the required angle of launch for a desired range can be calculated from the motion equations.

From the range relationship, the angle of launch can be determined. For range R = m = ft, and launch velocity v0 = m/s = ft/s. there are two solutions for the launch angle. θ1 = degrees, θ2 = degrees,