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Velocity components of a throw

A throw without air resistance can be split into two motions that happen at the same time. Horizontally the velocity is constant, because no force acts that way. Vertically it is free fall, with the acceleration of gravity downwards. An initial velocity slanting upwards is split into a horizontal and a vertical component with the cosine and the sine of the angle to the ground. The time is the same in both directions, and it links them.

Try it yourself

Projectile motion

v_{0x} = v_0\cos\alpha

horizontal initial velocity

v_{0y} = v_0\sin\alpha

vertical initial velocity

Symbols

$v_0$	initial speed	m/s
$\alpha$	angle to the horizontal	°

Example

A ball is thrown at 20 m/s at 30° to the ground.

$v_{0x} = 20\cos 30^\circ \approx 17.32$ m/s and $v_{0y} = 20\sin 30^\circ = 10$ m/s.

At 45° the two components are equal. At a small angle the horizontal one dominates.

Practise projectiles and motion in two dimensions for free →

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Part of Physics 2: Projectiles and motion in two dimensions.