projectiles formulas

BASIC TERMS use in projectiles formulas

When a particle is projected into the air,

then the particle is called a projectile.
the point from which the particle is projected is called the point of projection.

the angle that the direction in which it is projected makes with the horizontal plane through the point of projection is called the angle of projection;
the path which the particle describes is called its trajectory;
the distance between the point of projection and the point where the path meets any plane drawn through the point of projection is its range on the plane;
the time that elapses before it again meets the horizontal plane through the point of projection is called the time of flight.

the initial velocity with which the projectile is projected is called the velocity of projection.
the maximum height reached by a projectile during its motion is called greatest height.

Check out Physics Formulas and NCERT Solutions for class 12 Physics prepared by Physics Wallah.

LIST OF PROJECTILES FORMULA

Velocity and direction of motion after time ‘t’ v² = u² – 2ugt sinα + g²t² and tanθ =
Velocity and direction of motion at height ‘h’ v² = u² – 2gh and tan θ =
Greatest height attained by a projectile h =

Time for the greatest height =
Time of flight t =
Range =
Maximum Range =

Here u : initial velocity of the body

α : Angle of projection

θ : Angle which the velocity of the projectile at a certain point makes with the horizontal (It is the tangent to the path of the projectile at the point)

g : acceleration due to gravity

Note:

The path of a projectile is a parabola, given by y = x tan α -

i.e. projectiles formulas

with vertex ≡

latus rectum =

and height of directrix =

The velocity at any point is equal in magnitude, to that which would be acquired by a particle in falling freely from the directrix to that point.
There are two direction for a given range and velocity and also two times for a given height.

Range and Time of Flight on an Inclined Plane:

If from a point on a plane which is inclined at an angle β to the horizon, a particle is projected with a velocity u, at an angle α with the horizontal, in a plane passing through the normal to the inclined plane and the line of greatest slope, then

Time of flight, T=
Range =
Maximum range up the plane =

Range, time of flight and maximum range down the plane is obtained by putting –β for β.
For a given range and given velocity there are two different directions of projection which are equally inclined to the direction of projection for maximum range.

Example :If the maximum range of a particle is R, show that the greatest height attained is . A body can throw a ball 60 meters. How long is the ball in the air, and what height does it attain.