Motion Under Gravity

All the body fall in the same acceleration due to gravity called acceleration of a free falling body denoted by letter g. it value is 10m/s² or 9.8m/s². Also distance moved by object changed to height because if falling

EQUATIONS OF FREE FALL

In the equations of motion discussed above are used in motion under fall by substituting “Acceleration due to gravity, “g” in “a” as shown below;

Now:  a = +g

           s = h

FIRST EQUATION

From v = u + at

Substitute a = g in the equation above

  Hence, v = u + gt

v =u+gt

SECOND EQUATION

From S = ut + ½(at²)

Substitute a = g in the equation above

S = ut + ½gt²

THIRD EQUATION

From v² = u² + 2as

  Substitute a = g in the equation above

v² = u² + 2gs

The equations of the free fall are;

i)       v = u + gt

ii)    h = ut + ½gt²

iii)   v² = u² + 2gh

Note:

a)      When the body falling down (a = g)

v = u + gt

h = ut + ½(gt²)

v² = u² + 2ah

At maximum height, u = 0 m/s

b)      When the body thrown up/vertical (a = -g)

v = u - gt

h = ut - ½(gt²)

v² = u² – 2gh

At maximum height, v = 0 m/s

Example1

A stone is dropped from the top of a building 180 m high. Determine;

a)      The time it takes to reach the ground

b)      The velocity with which it hits the ground

Solution

Data given 

Distance (s) = 180 m

Acceleration due to gravity (g) = 10 m/s²

Time (t) =?

Final velocity (v) =?

a)      From the second equation of free fall;

The time it takes to reach the ground = 6 seconds

b)      From the first equation

The velocity with which it hits the ground = 60 m/s

Example 2

A ball is thrown vertically upwards with a velocity of 50 m/s. Determine the maximum height it will attain. 

Solution

Data given

Initial velocity (u) = 50 m/s

Final velocity (v) = 0 m/s

Acceleration due to gravity (g) = 10 m/s²

Maximum height (s) =?

From the third equation

v² = u² + 2as

But when the ball moves vertically upwards, g = -10 m/s²

The maximum height it will attain = 125 m