Attribution: Cmglee, CC BY-SA 3.0, via Wikimedia Commons. Trajectories of projectiles launched at different elevation angles but at the same speed (g = 10 m/s²). Vertical motion under the influence of gravity can be described by the basic motion equations. If you've used the trigonometric functions calculator, you know that sin(2 x) = 2sin( x)cos( x), so we can write the final formula as: Velocity, in our case, is the horizontal velocity V x = V₀ × cos(α), and the time to reach the ground is a value we've already calculated:ĭ = V × t = V₀ × cos( α) × 2 × V₀ × sin( α)/ g Given the constant acceleration of gravity g, the position and speed at any time can be calculated from the motion equations: You may enter values for launch velocity and time in the boxes below and click outside the box to perform the calculation. The projectile range is the distance traveled by the object when it returns to the ground (so y = 0):įrom that equation, we'll find t, which is the time of flight to the ground:Īlso, we know that we can find the maximum distance of the projectile from the widely known formula: d = V × t (learn more in our distance calculator). Vertical motion under the influence of gravity can be described by the basic motion equations. To find the formula for the projectile range, let's start with the equation of motion. The components of the initial velocity ( v0x, v0y) of a projectile when the magnitude of initial velocity v0 and the initial angle to the horizontal direction are given. Inputs: initial vertical velocity (v y0) acceleration of gravity (g) Are you able to help others Share this page. The Calculator calculates: Initial Horizontal Velocity (Vx) Initial Vertical Velocity (Vy) Gravitational Acceleration. The position ( x, y) of a projectile at any instant t during its motion when the initial velocity v 0 and the initial angle to the horizontal direction are given. Launch from the ground (initial height = 0) Projectile Motion Equations Calculator Science Physics Formulas Solving for vertical velocity at time. Let's split the equations into two cases: when we launch the projectile from the ground and when the object is thrown from some initial height (e.g., table, building, bridge).ġ.
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