So to reach the maximum height by the projectile the time taken is (V 0sinθ )/g It can be proved that the projectile takes equal time to come back to the ground from its maximum height. Total time of flight for a projectile & Formula Try this formula at our Projectile Motion online Calculator So this is the equation for the time required to reach the maximum height by the projectile. The initial velocity for the motion along Y-axis (as said above) is V 0sinθĬonsidering vertical motion along the y-axis: Say the time required to reach this maximum height is t max. When the projectile reaches the maximum height then the velocity component along Y-axis i.e. Time to reach the Maximum Height by a projectile (with derivation for class 11) projectile motion: components of initial velocity V 0 the trajectory of projectile – a parabolic path Hence we can say that trajectory of a projectile will follow a curve that is represented as Parabola. This is again an equation that represents Parabola. x 2/(V 0 cosθ) 2 As you see this can be rewritten in the form y = ax + bx 2 where a and b are constants. So once thrown at an angle (excluding the right angle) with the horizontal, a projectile will follow a curved path named Parabola.Įquation of the Trajectory of a projectile is a parabolaįrom equation 4 above, we get the trajectory path of a projectile as y = (tanθ) x – (1/2) g. So we can say that the trajectory or motion path of a projectile is a parabola. This is an equation representing a parabola. So rewriting equation 4: y = ax + bx 2 where a and b are constants. In the above equation g, θ, and V 0 are constant. Replacing t in equation 2 with the expression of t from equation 3: (Air resistance is taken as negligible)Īt time T = 0, there is no displacement along the X and Y axes.Īt time T=t, (i.e., for any time instant t) Displacement along X-axis = x= V 0x.t = (V 0 cosθ). The initial velocity component along X-axis = V 0x = V 0 cosθ and the initial velocity component along Y-axis = V 0y = V 0sinθ. Showing initial velocity V 0 and its components along the X and Y axes for a projectile motion (Velocity components when time t =0) Say an object is thrown with uniform velocity V 0 making an angle theta with the horizontal (X) axis. Let’s start with the derivation of the Projectile Motion Path Equation (or Projectile trajectory equation). See also How to determine Acceleration on displacement-time graphs In the absence of air resistance, the path of the flight of a projectile will trace out the shape of a parabola as shown by the photograph in one of the figures below, taken with the aid of a stroboscope. The trajectory of a projectile is the path that it follows during its flight. Students of Class 11 from boards like ISC, CBSE, and state boards will find this one useful.ĭerivation of the trajectory equation | Derive projectile trajectory or path formula class 11 We will cover here Projectile Motion Derivation to derive a couple of equations or formulas like:ġ> derivation of the projectile path equation (or trajectory equation derivation for a projectile)Ģ> Derivation of the formula for time to reach the maximum heightģ> Total time of flight – formula derivationĤ> Maximum height of a projectile – formula derivation andĥ> Derivation of the formula for the horizontal range of a projectile Projectile Motion Derivation | Derivation of Projectile Motion Equations class 11 In the next sections, we will discuss and derive a couple of projectile motion equations. One component is along a horizontal direction without any acceleration (as no force acting in this direction) and the other is along the vertical direction with constant acceleration due to the force of gravity (considering air resistance as negligible). The motion of a projected object in flight is known as projectile motion which is a result of 2 separate simultaneously occurring components of motion. For example, the motions of a cricket ball, or baseball. When an object is in flight after being projected or thrown then that object is called a projectile and this motion is called Projectile Motion. Projectile motion – showing initial velocity V 0 and its components along the X and Y axes. When an object is in flight after being projected or thrown then that object is called a projectile and this motion under the influence of constant velocity along the horizontal and downward gravitational pull along the vertical is called Projectile Motion.
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