Projectile Motion

Projectile Motion

When an object is thrown/launched/fired on the Earth's surface, it will experience a downwards Force due to Gravity. The path the object takes through the air is a combination of the forward motion and the downwards motion. This results in the projectile (object being projected) following a curved path through the air.

Each of these motions are independent of each other, leading to some counterintuitive results. For example, If a bullet cartridge drops out of a gun at the instant the gun is fired, both the bullet and the cartridge will hit the ground at the same time.

The video below shows the "Monkey and the Hunter" thought experiment based upon Projectile Motion theory:-

For all Projectile Motion :-

1. Constant horizontal Velocity - No unbalanced Forces acting.

2. Constant vertical Acceleration - Acceleration due to Gravity (a = 9.8 ms-2).

Note - At National 5 Level it is assumed there is no air resistance, allowing constant horizontal Velocity.

In order to calculate the path taken by a projectile, each component of motion must be taken independently :-

Example 1 -

A ball is kicked horizontally from the top of a cliff as shown below :-

If its initial Horizontal velocity is 10 ms-1, and it takes 4 seconds to hit the ground, calculate the following :-

1. How far from the base of the cliff does the ball land.

2. The vertical Velocity at the moment of Impact.

The Height of the cliff

Step 1 - Identify known information in each plane

Horizontally :-

vh = 10 ms-1

t = 4 s

sh = ?

Vertically :-

uv = 0 ms-1

vv = ?

a = - 9.8 ms-2

sv = ?

t = 4 s

Step 2 - Calculate in each plane separately :-

vh = sh / t

sh = vh x t

sh =10 x 4

sh = 40 m

vv = uv + at

vv = 0 + (-9.8 x 4)

vv = -39.2 ms-1

vv = 39.2 ms-1 (downwards)

s = ut + 0.5 x a t2

s = 0 + (0.5 x -9.8 x 42)

s = -78.4 m

s = 78.4 m (downwards)