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 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). To find the formula for the projectile range, let's start with the equation of motion. Launch from the ground (initial height = 0) You may also find the following Physics calculators useful.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. 4.4 - Types of Forces III (Elastic Force and Tension).4.1 - What Causes Motion? The Meaning of Force.Please provide a rating, it takes seconds and helps us to keep this resource free for all to useĭynamics Physics Tutorials Associated with the Projectile Motion Calculator This allows us to allocate future resource and keep these Physics calculators and educational material free for all to use across the globe. We hope you found the Projectile Motion Calculator useful, if you did, we kindly request that you rate this calculator and, if you have time, share to your favourite social network. You can then email or print this motion calculation as required for later use. As you enter the specific factors of each projectile motion calcualtion, the Projectile Motion Calculator will automatically calculate the results and update the formula elements with each element of the projectile motion calculation. Please note that the formula for each calculation along with detailed calculations is shown further below this page. Magnitude of the Velocity at a Given Instant ( |v|) m/sĪngle formed by the Instantaneous Velocity Vector and the Horizontal Direction ( α) ° Vertical Component of the Instantaneous Velocity at a Given Instant ( v y) m/s Vertical Position of the Object at a Certain Instant ( y(t)) m Horizontal Position of the Object at a Certain Instant ( x(t)) m Vertical Component of the Initial Velocity ( v 0y) m/s Projectile Motion Calculator Results (detailed calculations and formula below) Horizontal Component of the Initial Velocity ( v 0x) m/s Magnitude of the Object's Initial Velocity ( |v 0|) m/s Initial Vertical Position of the Object ( y 0) m Initial Horizontal Position of the Object ( x 0) m Projectile Motion Calculator □ Normal View □ Full Page View The maximum height h max the projectile can reach during its flight when the initial velocity v 0 and the initial angle θ to the horizontal direction are given.The acute angle α formed by the projectile and the horizontal direction at any instant t during its motion when the initial velocity v 0 and the initial angle θ to the horizontal direction are given.The magnitude of the instantaneous velocity |v| at a given instant t.The components of instantaneous velocity ( v x, v y) of a projectile at any instant t during its motion when the magnitude of initial velocity |v 0| and the initial angle θ to the horizontal direction are given.The components of the initial velocity ( v 0x, v 0y) of a projectile when the magnitude of initial velocity |v 0| and the initial angle θ to the horizontal direction are given.The position ( x, y) of a projectile at any instant t during its motion when the initial velocity v 0 and the initial angle θ to the horizontal direction are given.The acceleration caused by these forces on the object.The resultant of all forces acting on an object.A list of the supporting Dynamics Physics Tutorials is available at the bottom of this page. The Projectile Motion Calculator is provided in support of our Physics Tutorials on Dynamics which explore Motion, the meaning of force, types of forces including gravitational force and weight, resistive forces, terminal velocity, elastic force and tension, inertia and explain Newtons Laws of Motion in clear detail with practical working examples and formula.
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