<< Chapter < Page Chapter >> Page >

Introduction

In Grade 10, we studied motion in one dimension and briefly looked at vertical motion. In this chapter we will discuss vertical motion and also look at motion in two dimensions. In Grade 11, we studied the conservation of momentum and looked at applications in one dimension. In this chapter we will look at momentum in two dimensions.

Vertical projectile motion

In Grade 10, we studied the motion of objects in free fall and we saw that an object in free fall falls with gravitational acceleration g . Now we can consider the motion of objects that are thrown upwards and then fall back to the Earth. We call this projectile motion and we will only consider the situation where the object is thrown straight upwards and then falls straight downwards - this means that there is no horizontal displacement of the object, only a vertical displacement.

Motion in a gravitational field

When an object is in the earth's gravitational field, it always accelerates downwards, towards the centre of the earth, with a constant acceleration g , no matter whether the object is moving upwards or downwards. This is shown in [link] .

Projectiles moving upwards or downwards in the earth's gravitational field always accelerate downwards with a constant acceleration g . Note: acceleration means that the velocity changes ; it either becomes greater or smaller.
Objects moving upwards or downwards, always accelerate downwards.

This means that if an object is moving upwards, its velocity decreases until it stops ( v f = 0  m · s - 1 ). This is the maximum height that the object reaches, because after this, the object starts to fall.

Projectiles have zero velocity at their greatest height.

Consider an object thrown upwards from a vertical height h o . We have seen that the object will travel upwards with decreasing velocity until it stops, at which point it starts falling. The time that it takes for the object to fall down to height h o is the same as the time taken for the object to reach its maximum height from height h o .

(a) An object is thrown upwards from height h 0 . (b) After time t m , the object reaches its maximum height, and starts to fall. (c) After a time 2 t m the object returns to height h 0 .
Projectiles take the same time to go from the point of launch to the greatest height as the time they take to fall back to the point of launch.

Equations of motion

The equations of motion that were used in Chapter  [link] to describe free fall can be used for projectile motion. These equations are the same as those equations that were derived in Chapter  [link] , but with acceleration from gravity: a = g . We use g = 9 , 8 m · s - 2 for our calculations.

Remember that when you use these equations, you are dealing with vectors which have magnitude and direction. Therefore, you need to decide which direction will be the positive direction so that your vectors have the correct signs.

v i = initial velocity ( m · s - 1 ) at time t = 0 s v f = final velocity ( m · s - 1 ) at time t Δ x = vertical displacement ( m ) t = time ( s ) Δ t = time interval ( s ) g = acceleration due to gravity ( m · s - 2 )
v f = v i + g t Δ x = ( v i + v f ) 2 t Δ x = v i t + 1 2 g t 2 v f 2 = v i 2 + 2 g Δ x

Questions & Answers

if three forces F1.f2 .f3 act at a point on a Cartesian plane in the daigram .....so if the question says write down the x and y components ..... I really don't understand
Syamthanda Reply
hey , can you please explain oxidation reaction & redox ?
Boitumelo Reply
hey , can you please explain oxidation reaction and redox ?
Boitumelo
for grade 12 or grade 11?
Sibulele
the value of V1 and V2
Tumelo Reply
advantages of electrons in a circuit
Rethabile Reply
we're do you find electromagnetism past papers
Ntombifuthi
what a normal force
Tholulwazi Reply
it is the force or component of the force that the surface exert on an object incontact with it and which acts perpendicular to the surface
Sihle
what is physics?
Petrus Reply
what is the half reaction of Potassium and chlorine
Anna Reply
how to calculate coefficient of static friction
Lisa Reply
how to calculate static friction
Lisa
How to calculate a current
Tumelo
how to calculate the magnitude of horizontal component of the applied force
Mogano
How to calculate force
Monambi
a structure of a thermocouple used to measure inner temperature
Anna Reply
a fixed gas of a mass is held at standard pressure temperature of 15 degrees Celsius .Calculate the temperature of the gas in Celsius if the pressure is changed to 2×10 to the power 4
Amahle Reply
How is energy being used in bonding?
Raymond Reply
what is acceleration
Syamthanda Reply
a rate of change in velocity of an object whith respect to time
Khuthadzo
how can we find the moment of torque of a circular object
Kidist
Acceleration is a rate of change in velocity.
Justice
t =r×f
Khuthadzo
how to calculate tension by substitution
Precious Reply
hi
Shongi
hi
Leago
use fnet method. how many obects are being calculated ?
Khuthadzo
khuthadzo hii
Hulisani
how to calculate acceleration and tension force
Lungile Reply
you use Fnet equals ma , newtoms second law formula
Masego
please help me with vectors in two dimensions
Mulaudzi Reply
how to calculate normal force
Mulaudzi
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Siyavula textbooks: grade 12 physical science. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11244/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Siyavula textbooks: grade 12 physical science' conversation and receive update notifications?

Ask