# 0.4 2.5 projectile motion

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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 $\mathbf{s}$ is defined to be the total displacement and $\mathbf{x}$ and $\mathbf{y}$ 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 $\mathbf{A}$ to represent a vector with components ${\mathbf{A}}_{x}$ and ${\mathbf{A}}_{y}$ . If we continued this format, we would call displacement $\mathbf{s}$ with components ${\mathbf{s}}_{x}$ and ${\mathbf{s}}_{y}$ . However, to simplify the notation, we will simply represent the component vectors as $\mathbf{x}$ and $\mathbf{y}$ .)

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: ${a}_{y}=–g=–9.80 m{\text{/s}}^{2}$ . (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, ${a}_{x}=0$ . Both accelerations are constant, so the kinematic equations can be used.

## Review of kinematic equations (constant $a$ )

$x={x}_{0}+\stackrel{-}{v}t$
$\stackrel{-}{v}=\frac{{v}_{0}+v}{2}$
$v={v}_{0}+\text{at}$
$x={x}_{0}+{v}_{0}t+\frac{1}{2}{\text{at}}^{2}$
${v}^{2}={v}_{0}^{2}+2a\left(x-{x}_{0}\right)\text{.}$

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what are the products of Nano chemistry?
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learn
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da
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Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
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da
Application of nanotechnology in medicine
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I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
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Professor
I think
Professor
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Alexandre
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Alexandre
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Rafiq
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Damian
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What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
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?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
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Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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An helicopter is flying over new York with a horizontal component of velocity of 14.6m/s-1 and a vertical component of -8.62 m/s-1, calculate, (a), the magnitude of the total velocity of the helicopter. (b), the angle of the total velocity.