![]() ![]() ![]() The second number is the time it takes to fall from the top of the trajectory onto the target area. For easier mathematical manipulation I'll write $y_0$ for "initial position $y$", $v_,$ is the time it takes from the instant of the launch until the projectile reaches the top of its trajectory. Launch from the ground (initial height 0) To find the formula for the projectile range, let's start with the equation of motion. These are the same calculations that the "regular" formulas come from,Įxcept that the "up" and "down" parts are not equal.Īlternatively, you can use your formula for height. The total flight time is the time going up plus the time going down.ĭuring the total flight time, the projectile continues moving at the same horizontal velocity. You also compute the height at the top of the trajectory (initial height plus height gained during the time you just calculated).įrom the height at the top of the trajectory, and the height of the impact area (I'm guessing this is zero for your problem, since you only said the initial height was not zero), you compute the amount of time spent falling. 1 - Projectile Motion Calculator and Solver Given Initial Velocity, Angle and Height Enter the initial velocity V0 in meters per second (m/s), the initial andgle in degrees and the initial height y0 in meters (m) as positive real numbers and press 'Calculate'. To treat such problems, the same principles that were discussed earlier in Lesson 2 will have to be combined with the kinematic equations for projectile motion. (That is, we pretend the Earth is flat and non-rotating.)Īssuming the initial firing direction is at some upward angle, you have an initial upward velocity component and an initial forward velocity component.įrom the initial height and upward velocity you compute the time until the top of the trajectory, when the projectile has zero vertical velocity. A non-horizontally launched projectile is a projectile that begins its motion with an initial velocity that is both horizontal and vertical. ![]() I'll make the usual first-year physics assumptions that there is no air resistance and no effects from the curvature of the Earth or from the Earth's rotation. ![]()
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