Motion under gravity

The force of gravity pulls on all objects on Earth. If all objects are allowed to fall, they will accelerate downwards.  If there is no air resistance, then all objects would fall at the same rate.  

Acceleration due to gravity = 9.8 m/s².  For simplicity 10 m/s² is usually used.

This means that for an object falling with no air resistance, the velocity after 1 second is 10 m/s, after 2 seconds velocity is 20 m/s and so on.

Image: IFP news. (2015). Available online here. CC BY 4.0)

In practice, there usually is air resistance. If the skydiver in the photo falls a long way without a parachute, then because of friction she reaches a final or terminal velocity of about 50 m/s, which is the same speed as a fast racing car.

Raindrops, snowflakes and seeds for example, all fall at their own terminal velocity.

A parachute is designed to make the air resistance as large as possible. With a parachute the terminal velocity is 8 m/s. 

Image: Pxhere (CC0 PD)

At terminal velocity, the forces on the object are balanced:

Force of gravity (weight) = force of air resistance

    (downwards)                        (upwards)

This is an example of Newton’s first law, because there is no resultant force on the object, it continues to move at a constant speed in a straight line. 

Example:

A ball is thrown vertically upwards at 20 m/s.  Ignoring air resistance and taking gravity = 10 m/s², calculate:

a)    How high it goes.

b)    The time taken to reach this height.

c)    The time taken to return to its starting point. 

When travelling upwards it is decelerating so a = - 10 m/s².

At the moment when it reaches its highest point, v = 0.

Write:

s = ?

u = 20 m/s

v = 0

a = - 10 m/s²

t = ?

a)  v² = u² + 2as

0 = 20² + 2(-10)s

20s = 20²

s = 20 m

b)  v = u + at

0 = 20 + (-10) t

t = 2 seconds

c) It also takes 2 seconds to fall down again, so in time take to return to its starting point = 4 seconds.