General Ballistic Trajectory The motion of an object under the influence of gravity is determined completely by the acceleration of gravity, its launch speed, and launch angle provided air friction is negligible. The values below are output values those boxes will not accept input for calculation.The velocity will beĪll the parameters of a horizontal launch can be calculated with the motion equations, assuming a downward acceleration of gravity of 9.8 m/s 2.Ĭalculation is initiated by clicking on the formula in the illustration for the quantity you wish to calculate. You may enter values for launch velocity and time in the boxes below and click outside the box to perform the calculation.For launch speed v 0y = m/s= ft/s Given the constant acceleration of gravity g, the position and speed at any time can be calculated from the motion equations: Vertical motion under the influence of gravity can be described by the basic motion equations. But the calculation assumes that the gravity acceleration is the surface value g = 9.8 m/s 2, so if the height is great enough for gravity to have changed significantly the results will be incorrect. 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. ![]() The distance from the starting point will beĮnter data in any box and click outside the box. Since all the quantities are directed downward, that direction is chosen as the positive direction in this case. Its position and speed can be predicted for any time after that. Illustrated here is the situation where an object is released from rest. Position and speed at any time can be calculated from the motion equations. In the absence of frictional drag, an object near the surface of the earth will fall with the constant acceleration of gravity g. Wait until it finishes loading for full functionality. The time of flight T f is found by solving the equationįor t and taking the largest positive solution.Trajectories Note: This is a large HTML document. Hence the maximum height y max reached by the projectile is given by The time T m at which y is maximum is at the vertex of y = y 0 + V 0 sin(θ) t - (1/2) g t 2 and is given by The displacement is a vector with the components x and y given by: V x = V 0 cos(θ) and V y = V 0 sin(θ) - g t The vector acceleration A has two components A x and A y given by: (acceleration along the y axis only)Īt time t, the velocity has two components given by The vector initial velocity has two components: V 0x and V 0y given by: Projectile Equations used in the Calculator and Solver ![]() Range = 50m, Initial Velocity: V 0 = 30m/s, Initial Height: y 0 = 10mĭecimal Places = 4 Initial Angle = ° Maximum Height = meters Flight Time= seconds Equation of the Path:: y = x 2 + x + The outputs are the initial angle needed to produce the range desired, the maximum height, the time of flight, the range and the equation of the path of the form \( y = A x^2 + B x + C\) given V 0 and y 0. Initial Velocity: V 0 = 30m/s, Initial Angle: θ = 50°, Initial Height: y 0 = 10mĭecimal Places = 4 Maximum Height = meters Flight Time= seconds Range = meters Equation of the Path: y = x 2 + x +Ģ - Projectile Motion Calculator and Solver Given Range, Initial Velocity, and Height Enter the range in meters, the initial velocity V 0 in meters per second and the initial height y 0 in meters as positive real numbers and press "Calculate". ![]() The outputs are the maximum height, the time of flight, the range and the equation of the path of the form \( y = A x^2 + B x + C\). The projectile equations and parameters used in this calculator are decribed below.ġ - Projectile Motion Calculator and Solver Given Initial Velocity, Angle and Height Enter the initial velocity V 0 in meters per second (m/s), the initial andgle θ in degrees and the initial height y 0 in meters (m) as positive real numbers and press "Calculate". An online calculator to calculate the maximum height, range, time of flight, initial angle and the path of a projectile.
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