![]() ![]() ![]() The second number is the time it takes to fall from the top of the trajectory onto the target area. Below I explain how this calculation is done within the app. Physics Equation - cannot solve for theta 1. 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. your phone at the base of an object and then the app gives you the distance to that object. How do you calculate the Range and Flight Time of a trajectory if the initial height is greater than zero (assuming youre in a vacuum) The regular formulas I come across dont take initial height into account. I apologize my equation is all over the place but anything close would help. The horizontal range of a projectile is the distance along the horizontal plane it would travel, before reaching the same vertical position as it started from. 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. Calculates the free fall distance and velocity without air resistance from. Writing down all of the known information is the. The range equation is derived from the kinematic equations assuming a constant downward acceleration equal to g and zero horizontal acceleration. 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. In order to solve any physics problem you must know which equation to use. The range equation (below) allows us to predict the launch distance, or range, from the launch angle and launch speed. 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. (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. 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. The range of the projectile is the total horizontal distance traveled during the flight time.
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