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  • Identify and explain the properties of a projectile, such as acceleration due to gravity, range, maximum height, and trajectory.
  • Determine the location and velocity of a projectile at different points in its trajectory.
  • Apply the principle of independence of motion to solve projectile motion problems.

Projectile motion is the motion    of an object thrown or projected into the air, subject to only the acceleration of gravity. The object is called a projectile    , and its path is called its trajectory    . The motion of falling objects, as covered in Problem-Solving Basics for One-Dimensional Kinematics , is a simple one-dimensional type of projectile motion in which there is no horizontal movement. In this section, we consider two-dimensional projectile motion, such as that of a football or other object for which air resistance     is negligible .

The most important fact to remember here is that motions along perpendicular axes are independent and thus can be analyzed separately. This fact was discussed in Kinematics in Two Dimensions: An Introduction , where vertical and horizontal motions were seen to be independent. The key to analyzing two-dimensional projectile motion is to break it into two motions, one along the horizontal axis and the other along the vertical. (This choice of axes is the most sensible, because acceleration due to gravity is vertical—thus, there will be no acceleration along the horizontal axis when air resistance is negligible.) As is customary, we call the horizontal axis the x -axis and the vertical axis the y -axis. [link] illustrates the notation for displacement, where s size 12{s} {} is defined to be the total displacement and x size 12{x} {} and y size 12{y} {} are its components along the horizontal and vertical axes, respectively. The magnitudes of these vectors are s , x , and y . (Note that in the last section we used the notation A size 12{A} {} to represent a vector with components A x size 12{A rSub { size 8{x} } } {} and A y size 12{A rSub { size 8{y} } } {} . If we continued this format, we would call displacement s size 12{s} {} with components s x size 12{s rSub { size 8{x} } } {} and s y size 12{s rSub { size 8{y} } } {} . However, to simplify the notation, we will simply represent the component vectors as x size 12{x} {} and y size 12{y} {} .)

Of course, to describe motion we must deal with velocity and acceleration, as well as with displacement. We must find their components along the x - and y -axes, too. We will assume all forces except gravity (such as air resistance and friction, for example) are negligible. The components of acceleration are then very simple: a y = g = 9.80 m /s 2 size 12{a rSub { size 8{y} } ="-g"="-9.80" "m/s" rSup { size 8{2} } } {} . (Note that this definition assumes that the upwards direction is defined as the positive direction. If you arrange the coordinate system instead such that the downwards direction is positive, then acceleration due to gravity takes a positive value.) Because gravity is vertical, a x = 0 size 12{a rSub { size 8{x} } } {} . Both accelerations are constant, so the kinematic equations can be used.

Review of kinematic equations (constant a )

x = x 0 + v - t size 12{x=`x rSub { size 8{0} } `+` { bar {v}}t} {}
v - = v 0 + v 2 size 12{ { bar {v}}=` { {v rSub { size 8{0} } +v} over {2} } } {}
v = v 0 + at size 12{v=v rSub { size 8{0} } + ital "at"} {}
x = x 0 + v 0 t + 1 2 at 2 size 12{x=x rSub { size 8{0} } +v rSub { size 8{0} } t+ { {1} over {2} } ital "at" rSup { size 8{2} } } {}
v 2 = v 0 2 + 2 a ( x x 0 ) . size 12{v rSup { size 8{2} } =v rSub { size 8{0} } rSup { size 8{2} } +2a \( x - x rSub { size 8{0} } \) } {}
A soccer player is kicking a soccer ball. The ball travels in a projectile motion and reaches a point whose vertical distance is y and horizontal distance is x. The displacement between the kicking point and the final point is s. The angle made by this displacement vector with x axis is theta.
The total displacement s size 12{s} {} of a soccer ball at a point along its path. The vector s size 12{s} {} has components x size 12{x} {} and y size 12{y} {} along the horizontal and vertical axes. Its magnitude is s size 12{s} {} , and it makes an angle θ size 12{θ} {} with the horizontal.

Questions & Answers

what is fluid
Anthony Reply
anything that flows is Liquid.
a substance that has no specific shape
How submarines floats one water the same time sink in water
Courage Reply
A submarine has the ability to float and sink. The ability to control buoyancy comes from the submarine'strim or ballast tanks which can be filled with either water or air, depending on whether the submarine needs to floator sink. When the submarine floats it means its trim tanks are filled with air
what is work
Ojo Reply
Force times distance
product of force and distance...
Is physics a natural science?
Adebisi Reply
what is the difference between a jet engine and a rocket engine.
Samuel Reply
explain the relationship between momentum and force
Joseph Reply
A moment is equivalent multiplied by the length passing through the point of reaction and that is perpendicular to the force
How to find Squirrel frontal area from it's surface area?
Pooja Reply
how do we arrange the electronic configuration of elements
Muhammed Reply
hi guys i am an elementary student
benedict Reply
are you an elementary student too?
no bro
what is the four equation of motion
what is strain?
Change in dimension per unit dimension is called strain. Ex - Change in length per unit length l/L.
strain is the ratio of extension to length..=e/l...it has no unit because both are in meters and they cancel each other
How is it possible for one to drink a cold drink from a straw?
Karanja Reply
most possible as it is for you to drink your wine from your straw
state the law of conservation of energy
Sushma Reply
energy can neither be destroy or created,but can be change from one form to another
it can neither be created nor destroyed
its so sample question dude
what is the difference between a principle and a law?
Mary Reply
where are from you wendy .?
you are beautiful
are you physics student
laws are ment to be broken
hehe ghulam where r u from?
principle are meant to be followed
south Africa
here Nigeria
principle is a rule or law of nature, or the basic idea on how the laws of nature are applied.
Rules are meant to be broken while principals to be followed
principle is a rule or law of nature, or the basic idea on how the laws of nature are applied.
what is momentum?
prakash Reply
is the mass times velocity of an object
it is the product of mass and velocity of an object.
The momentum possessed by a body is generally defined as the product of its mass and velocity m×v
momentum is the product of the mass of a body of its velocity
what about kg it is changing or not
vijay Reply
no mass is the quantity or amount of body so it remains constant everywhere
remains constant
mass of an object is always constant. and that is universally applied.
mass of a body never changes but the weight can change due to variance of gravity at different points of the world
what is hookes law
mass of an object does not change
Is weight a scalar quantity
esther Reply
weight is actually a force of gravity with which earth attracts us downwards so it is a vector quantity. and it has both direction and magnitude
weight is the earth pull of the body
why does weight change but not mass?
Theo, the mass of an object can change but it depends on how you define that object. First, you need to know that mass is the amount of matter an object has, and weight is mass*gravity (the "force" that attracts object A to the object B mass).
So if you face object A with object B, you will get a different result than facing object A with object C, so the weight of object A changes but not its mass.
Now, if you have an object and you take a part away from it, you are changing it mass. Lets use the human body and fat loss process as an example.
When you lose weight by doing exercise, you are being attracted by the same object before and after losing weight so the change of weight is related to a change of mass not a change of gravity.
The explanation of this is simple, we are composed of smaller particles, which are itself objects, so the loose of mass of an object actually is the separation of one object is two different ones.
But if you define an object because of its form and characteristics and not the amount of mass, then the object is the same but you have taken a part of it mass away.
Theo, weight =mass. gravity, here mass is fixed everywhere but gravity change in different places so weight change not mass.
yup weight changes and mass does not. That's why we're 1/3 our weight on the moon
weight is the product of mass × velocity w=m×v = m(v-u) but v=u+1/2at^ weight is a scalar quantity mass of an obj is the amount of particles that obj cont
mass is fixed always while weight is dynamic
Why does water wet glass but mercury does not?
thanks guys
Yusuf Shuaibu, for water the Adhessive force between water molecules and glass is greater than the cohessive force between it's own molecules but for Mercury the cohessive force will be greater in comparison with adhessive force. For this water wet glass but Mercury does not.
Practice Key Terms 7

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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