![]() ![]() Here we will use the equation for the time of flight, i.e. It is the horizontal distance covered by the projectile during the time of flight. => h = 0 + (½) g T 2 Time of flight of a horizontal projectile = T = √(2h/g) …………… (4) Range of a horizontal projectile For the vertical downward movement of the body we use this equation: s y = u y + (½) g t 2 Upon reaching the peak, the projectile falls with a motion that is symmetrical to its path upwards to the peak. It is the total time for which the projectile remains in flight (from O to A). A projectile is launched at an angle to the horizontal and rises upwards to a peak while moving horizontally. Now if β is the angle which resultant velocity makes with the horizontal, then tanβ = v y/v x= gt / u => β = tan -1(gt/u) Time of flight of a projectile launched horizontally So at point P, v x = u ……………… (i)Ĭonsidering motion along vertical axis, v y = u y + g t As, initial velocity along Y axis = u y = 0, hence, v y = g t …………(ii) Magnitude of resultant velocity at any point P v 2 = v x 2 + v y 2 => So the equation of the horizontal projectile velocity is: v = √(v x 2 + v y 2) = √(u 2 + g 2 t 2) ……………. The velocity equation of the horizontal projectile | derive the equation of horizontal projectile velocityĪlong the horizontal axis,a x =0 so, velocity remains constant along horizontal axis. So, the trajectory of the projectile launched parallel to the horizontal is a parabola. (1) Now, Considering motion along Y axis, u y = 0 (initial velocity along Y axis, at t = 0) a y = g Now, distance traveled along the Y-axis can be expressed as: y = u y t + (½) g t 2 => y = (½) g t 2 ……………… (2) From 1 & 2 we get, y = (½) g t 2 => y = (½) g (x/u) 2 => y = x 2 Say, after a time duration of t the projectile reaches point P (x,y).Ĭonsidering motion with uniform velocity along X-axis, distance traveled along the X-axis in time t can be expressed as: See also How is Uniform Circular Motion called a motion with acceleration? Trajectory equation of the horizontal projectile & its derivation ![]()
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