**Motion Under Gravity | Motion Under Gravity Important Concepts**

A Body is Released From a Height Whenever a body is released frrom a height, it travels vertically downward towards the surface of earth.This is due to the force of gravitational attraction exerted on body by the eareth. The acceleration produced by this force is called acceleration due to gravity and is denoted by ‘g’. Value of ‘g’ on the surface of earth is taken to the 9.8 m/s2 and it is same for all the bodies. It means all bodies (whether an iron ball or a piece of paper), when dropped (u=0) from same height shoulfd fall with same rapidity and should take same time to reach the earth. Our daily observation is contrary to this concept. We find that iron ball falls more rapidlly than piece of paper. This is due to the presence of air which offers different resistance to them. In the absence of air both would have taken same time to reach the surface of earth.

**Motion Under Gravity: **When a body is dropped from some height (earth's radius = 6400 km), it falls freely under gravity with constant acceleration g (= 9.8 m/s2) provided the air resistance is negligible small. The same set of three equations of kinematics (where the acceleration \vec{a} remains constant) are used in solving such motion. Here, we replace \vec{a} by \vec{g} and choose the direction of y-axis conveniently. When the y-axis is chosen positive along vertically downward direction, we take \vec{g} as positive and use the equation as

A body is Dropped From Some Height

v = u + gt, v2 = u2 + 2gh, and h = ut + 1/2gt2

where h is the displacement of the body and u is initial velocity of projection in the vertically downward direction. However, if an object is projected vertically upward with initial velocity u, we can take y-axis positive in the vertically upward direction and the set of equations reduces to

v = u - gt, v2 = u2 - 2gh, and h = ut - 1/2gt2

In order to avoid confusion in selecting \vec{g}as positive or negative, it is advisable to take the y-axis as positive along vertically upward direction and point of projection as the origin. We can now write the set of three equations in the vector form:

**Did You Know **

- Acceleration of all these bodies is constant.
- Acceleration is always directed downward.
- All bodies, when dropped (u=0) from same height should fall with same rapidity and should take same time to reach the earth.

**Question 1**

A stone is released with zero velocity from the top of a tower reaches the ground in 4 second, the height of the tower is about

(a) 20 m (b) 40 m

**(c) 80 m ** (d) 16 m

**Question 2**

A stone is thrown vertically upwards with an initial velocity of 30 m/s. The time taken for the stone to rise to its maximum height is

(a) 0.326 s (b) 3.26 s

(c) 30.6 s ** (d) 3.06 s**

**Question 3**

Two balls are dropped from same height at 1 second interval of time. The separation between the two balls after 3 seconds of the drop of first ball is:

(a) 50 m (b) 40 m

(c) 35 m ** (d) 25 m**