Free Fall Formula
We know that the gravitational force acts on each and every object on earth.
Concept:
When we were holding the ball in our hand, the ball was experiencing this force but it was balanced by force that we were applying on it in opposite direction. Means ball is at rest means the initial velocity is zero. And once we release the ball from hands due to gravitational force of the ball falls under its influence.
“Whenever an object moves under the influence of force of gravity alone, it is said to falling freely”.
In this initial velocity is zero and velocity goes on increasing due to acceleration due to gravity.
The free fall is possible in vaccum.
The equation in free fall calculated by using Newton’s equation of motion.
Initial velocity = 0 (u)
Acceleration a = g
The equation of motion is, (i) V = u + at
So put the value of u = 0 and a = g
So, V = 0 + gt, V = gt —— (1)
Now for displacement
S = ut + ½ at2
u = 0, a = g
So, S = 0 + ½ gt2
S = ½ gt2 —— (2)
V2 = u2 + 2aS
u = 0, a = g
So, V2 = 0 + 2gs
V2 = 2gs ——- (3)
So, there are three equation in free fall
(1) V = gt
(2) S = ½ gt2
(3) V2 = 2gs
It the motion of an object is upward, then acceleration is negative i.e. direction is opposite to the velocity and value g is negative (-g).
Numericals on Free Fall
A basketball is thrown up and reaches at height of 5 m. What was its initial velocity? And how many time is required to come down?
Given g = 9.8 m/s2
motion is upward so final velocity V = 0
d = 5 m
acceleration (g) = (-g) = (9.8 m/s2)
motion is in upward so acceleration is –Ve
According to Newton’s 3rd equation of motion
V2 = u2 + 2as
O = u2 + 2 (-9.8) ×5
O + u2 + 19.6×5
∴ u2 = 98
u = √98
u = 9.8 m/s ‘
Then ball comes & it take t sec to come down so initial velocity u = 0
d = 5m, As the velocity and acceleration are in same direction,
a = g = 9.8 m/s2
According to Newton’s 2nd law of motion
S = ut + ½ at2
S = ut + ½ at2
5 = 0 + ½ 9.8 t2
t2 = 5/4.9
t2 = 1.02
t = 1.009 s
The basketball takes 1.009 S to reach the ground and same time for go up
So total time taken
= 2 × 1.009 = 2.018