Given the landing distance, angle, time of flight and ignoring air resistance, finding the initial velocity of a projectile, which is launched and lands on the same height of elevation, is quite easy. But what if the landing spot is on a higher elevation or the opposite? How will I add the "height" to the equation?


You can use the equation of trajectory for a projectile motion which is given as follows: $$y=xtan(\theta)+\frac{gx^2}{2u^2cos^2(\theta)}$$ Where you can take any launching or landing points by simply the $x$ and $y$ coordinates from the origin which is the launching point. Suppose you launched from a tower then simply add the height of the tower to the equation so it becomes something like : $$y=xtan(\theta)+\frac{gx^2}{2u^2cos^2(\theta)}+h$$ Here $\theta$ is the angle of launch, while $u$ is the speed of the launch. Note: Only take parts of the curve from $x=0$ Ofcourse you can calculate in others ways too like finding the horizontal displacement or the vertical displacement using the equations of motion if you know the information you’ve stated.

  • $\begingroup$ May I know from which app the image is taken from? $\endgroup$
    – user190068
    Mar 23 '18 at 7:55
  • $\begingroup$ It’s taken from an app called Desmos which is a graphing calculator. $\endgroup$ Mar 23 '18 at 7:59
  • $\begingroup$ Please accept the answer if you find it satisfactory! $\endgroup$ Mar 23 '18 at 8:01

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