Projectile Motion

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Projectile Motion

Advanced

If the final position is below the initial position, S is negative (provided up is the positive direction). Objects always move from initial position to final position and the direction of S can be found by drawing an arrow starting from initial position.

If the object is finally moving downards, V must be negative (provided up is the positive direction)

When an object is released, its initial velocity will be the velocity of the object that is releasing it (eg package dropped from a plane, or from a spinning wheel).

A projectile can have only an initial horizontal velocity and zero vertical velocity

Initial Velocity

The adjacent side always gets the cos(angle)

Draw a triangle and use the deifinition of sin and cos to work out components of the initial velocity vector

Use Usin(angle) and Ucos(angle) to break an initial U into the X and Y directions

Final Speed

Final Speed = Sqrt [(Vx)^2+ (Vy)^2]

Can be used to find the speed of the projectile at any location.

Use Pythagoras theorem

Is the Vector sum of Horizontal and Vertical Velocities

Y-Direction

At highest point, V=0. a is always known and is = -9.8 if upwards is the defined positive direction.

Substitute into correct SUVAT (Constant acceleration) Equation.

List out all known and unknown variables (U, V, a, t, S)

Define Positive (+) direction. Anything that acts downwards (eg acceleration, displacement) = -

X-Direction

Usually start with X direction to find time.

No acceleration. Therefore Initial speed=final speed

Equation: Speed=distance/time

Basics

Only time is common to both X and Y directional motion. Velocity, displacement, and acceleration are different. eg: velocity in y direction is different to speed in X direction.

Only 3 Variables in X-direction. Speed = Distance/time

Simplify projectiles into Horizontal Motion (x) and Vertical Motion (y)