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How to Find Horizontal Distance Without Initial Velocity
- 1). Calculate the initial velocity using the final velocity and the equation "vf = vi +at," where "at" is the acceleration of gravity (-9.8 m/s^2) multiplied by the time in seconds. If, for example, your projectile has a final velocity of 3.4 m/s and stays in the air for 5 seconds, you would set up the equation like so: 3.4 = vi + (-9.8)(5) = vi - 49; 3.4 + 49 = vi - 49 + 49. Your initial velocity, therefore, was 52.4 meters per second.
- 2). Calculate the horizontal component of the velocity. Set up a trigonometry problem considering the vertical and horizontal components of the velocity as sides of a triangle relative to the angle, θ, of the object's launch. Keeping in mind the basic trigonometric identities -- sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse; tan θ = opposite/adjacent -- you can then set the horizontal component of the velocity, or the one adjacent to the angle θ, equal to the total velocity v, or the hypotenuse, times cos θ, or: vh = v cos θ = hypotenuse * (adjacent/hypotenuse) = adjacent. If your launch angle is 60 degrees, compute this as follows: vh = v cos θ = 52.4 cos 60 = 52.4 * .5 = 26.2 m/s.
- 3). Multiply your horizontal velocity by time to get your horizontal distance. For the example problem, do this as follows: 26.2 * 5 = 131 meters.