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When working with projectile problems, the two most useful equations of motion are:
v = u + at and s = ut + \frac{1}{2}at^2 .
Remember that when the vertical component of velocity is positive, the particle is rising. At the instant this component is 0, the particle is at maximum height. When the vertical component of velocity is negative, the particle is falling.

For a projectile, the horizontal component of velocity is constant.
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Glossary

constant

a value in a formula or equation that cannot change.

particle

an object with negligible size and internal structure, which can be represented by a point; the fundamental assumption in mechanics.

projectile

a body moving in a gravitational field under free fall

union

The union of two sets A and B is the set containing all the elements of A and B.

velocity

the rate of change of displacement. It is a vector quantity with magnitude and direction.

Full Glossary List