Projectile Motion

Also called

projectile · parabola · parabolic path · range of a projectile · maximum range · angle of projection · 45 degrees · complementary angles · time of flight · maximum height · horizontal and vertical motion · independence of motions · velocity components · dropped and thrown ball · trajectory · प्रक्षेप्य गति · परवलय · परास

Topics

• The horizontal and vertical motions of a projectile are independent: gravity acts only on the vertical part.
• A ball thrown sideways and a ball dropped at the same instant fall together and hit the ground at the same time.
• The horizontal velocity stays constant, so the ball covers equal horizontal distances in equal times.
• The vertical velocity decreases to zero at the top and then grows downward: the path is a parabola.
• Range R = u² sin 2θ / g is greatest when sin 2θ = 1, that is at a projection angle of 45°.
• Angles that add to 90°, such as 30° and 60°, give the same range but different heights and times of flight.
• Time of flight T = 2u sin θ / g and maximum height H = u² sin² θ / 2g both grow with the angle of projection.
• At every point the velocity is the vector sum of a constant horizontal part and a changing vertical part.

About this model

A GLB file of about 630 KB, shown in Lably's 3D viewer and, on a phone, placed in your room with AR. Credit: Model, science and animation: Lably (built procedurally with three.js; no downloaded meshes). | CC BY 4.0. Original geometry and animation made for Lably.

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