of Cartesian coordinates. In this case, the position has the general formula . In this equation, the origin is the midpoint of the horizontal range of the projectile, and if the ground is flat, the parabolic arc is plotted in the range . This expression can be obtained by transforming the Cartesian equation as stated above by and . Properties of the trajectory Time of flight or total time of the whole journey The total time t for which the projectile remains in the air is called the time of flight. After the flight, the projectile returns to the horizontal axis (x-axis), so . Note that we have neglected air resistance on the projectile. If the starting point is at height y0 with respect to the point of impact, the time of flight is: As above, this expression can be reduced to if θ is 45° and y0 is 0. Time of flight to the target's position As shown above in the Displacement section, the horizontal and vertical velocity of a projectile are independent of each other. Because of this, we can find the time to reach a target using the displacement formula for the horizontal velocity: This equation will give the total time t the projectile must travel for to reach the target's horizontal displacement, neglecting air resistance. Maximum height of projectile The greatest height that the object will reach is known as the peak of the object's motion. The increase in height will last until , that is, . Time to reach the maximum height(h): . For the vertical displacement of the maximum height of projectile: The maximum reachable height is obtained for θ=90°: Relation between horizontal range and maximum height The relation between the range d on the horizontal plane and the maximum height h reached at is: × . Maximum distance of projectile The range and the maximum height of the projectile does not depend upon its mass. Hence range and maximum height are equal for all bodies that are thrown with the same velocity and direction. The horizontal range d of the projectile is the horizontal distance it has traveled when it returns to its initial height (). . Time to reach ground: . From the horizontal displacement the maximum distance of projectile: , so . Note that d has its maximum value when , which necessarily corresponds to , or . The total horizontal