Projectile Motion is a type of motion where a particle moves in a nonlinear path (a curved path) under the effects of gravity. The path this particle, called a projectile, follows is called it’s trajectory. Unless stated otherwise, the projectile will always be under the influence of gravity and follow normal physical laws. Solving projectile motion questions requires an understanding of putting vector quantities into their vertical and horizontal components.
The Initial Velocity, vo
If the projectile is launched with some initial velocity, vo, then it can be written as vo = voxi + voyj where i and j are the unit vectors in the horizontal and vertical directions, respectively. The components vox and voy can be found if the angle at which the the initial velocity if known, dented as α . You then use the formulas vox= vocos α and voy = vosinα.
Acceleration, a
Since, unless specified otherwise, there is no horizontal force acting on the projectile there is no horizontal acceleration therefore vox is constant. There is however vertical acceleration due to the effects of gravity. This means that ax=0 and ay=-g where g is the gravitational constant commonly equal to 9.8m/s2.
Velocity, v
As previously stated, there is no horizontal acceleration meaning the horizontal velocity remains constant. And the vertical velocity is accelerated by the effects of gravity and increases linearly as the gravity is considered constant. So at an time, t, the components of velocity are:
vx=v0cos (α) and vy=v0sin (α)-gt. To find the magnitude of the velocity can be found using the Pythagorean theorem: v = √(vx2+vy2).
Displacement
At any time, t, the projectile’s displacement can be found by looking at it’s horizontal and vertical components and use the following formulas: x=v0tcos(α) and y=v0tsin(α)-.5gt2.
This article was written for you by Troy, one of the tutors with SchoolTutoring Academy.