3.8 Projectile motion

Describe independent motion:

Take two balls. One ball dropped vertically and one is dropped horizontally. Both balls fall at the same rate, they are both at the same height at the same time. The horizontal and vertical motions are independent of each other.

Assuming no air resistance describe vertical and horizontal motion:

The vertical velocity changes due to acceleration of free fall.

The vertical displacement and time of flight can be calculated using equations of motion

Horizontal velocity remains constant

Why does horizontal velocity remain constant?

Acceleration and velocity are vectors. The acceleration of free fall is vertically downwards. The component of this acceleration in the horizontal direction is zero.

Horizontal Acceleration = gcos90⁰ = 0

Horizontal velocity is therefore unaffected by the fall.

How can the magnitude of the velocity of an object be calculated?

It can calculated from the vertical and horizontal components vx and vy of this velocity

Use pythagoras:

Actually velocity v = square root(vx² + vy²)

What is the angle made by velocity to the horizontal given by?

Angle theta = tan^-1 (vy/vx)

How can you find the components of the velocity when the path of a projectile is at an agle theta to the horizontal?

The initial velocity of the projectile is v.

The horizontal component of the velocity is vcostheta

The vertical component of the velocity is vsintheta