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Projectile thrown at an angle with horizontal direction

There are two possibilities. The projectile can be projected up or down as shown in the figure here :

Projection from an elevated level

Projection upwards from an elevated level
Projection downwards from an elevated level

Projectile thrown up at an angle with horizontal direction

The time of flight is determined by analyzing motion in vertical direction. The net displacement during the motion is equal to the elevation of point of projection above ground i.e. H 2 . To analyze the motion, we consider point of projection as origin, horizontal direction as x-axis and upward vertical direction as y-axis.

y = - H 2 = u y T 1 2 g T 2

Rearranging,

T 2 2 u y g T + 2 H 2 g = 0

This is a quadratic equation in “T”. Solving we get two values of T, one of which gives the time of flight.

An object projected up at an angle from an elevation

Horizontal range is given by analyzing motion in horizontal direction as :

x = R = u x T

While calculating maximum height, we can consider motion in two parts. The first part is the motion above the projection level. On the other hand second part is the projectile motion below projection level. The total height is equal to the sum of the magnitudes of vertical displacements :

H = | H 1 | + | H 2 |

Problem : A projectile is thrown from the top of a building 160 m high, at an angle of 30° with the horizontal at a speed of 40 m/s. Find (i) time of flight (ii) Horizontal distance covered at the end of journey and (iii) the maximum height of the projectile above the ground.

Solution : Unlike horizontal projection, the projectile has a vertical component of initial velocity. This vertical component is acting upwards, which causes the projectile to rise above the point of projection.

Here, we choose the point of projection as the origin and downward direction as the positive y – direction.

An object projected at an angle from an elevation

(i) Time of flight, T

Here,

u y = u sin θ = - 40 sin 30 0 = - 20 m / s ; y = 160 m ; g = 10 m / s 2

Using equation, y = u y t + 1 2 g t 2 , we have :

160 = - 20 t + 1 2 10 t 2 5 t 2 - 20 t - 160 = 0 t 2 - 4 t - 32 = 0 t 2 - 8 t + 4 t - 32 = 0 t ( t - 8 ) + 4 ( t - 8 ) = 0 t = - 4 s or t = 8 s

Neglecting negative value of time, T = 8 s.

(ii) Horizontal distance, R

There is no acceleration in horizontal direction. Using equation for uniform motion,

x = u x T

Here,

u x = u cos θ = 40 cos 30 0 = 20 3 m / s ; T = 8 s

x = u x T = 20 3 x 8 = 160 3 m

(iii) Maximum height, H

The maximum height is the sum of the height of the building ( H 2 ) and the height attained by the projectile above the building ( H 1 ).

H = H 1 + H 2

We consider vertical motion to find the height attained by the projectile above the building ( H 1 ).

H 1 = u 2 sin 2 θ 2 g

H 1 = 40 2 sin 2 30 0 2 X 10

H 1 = 40 2 X 1 4 2 X 10 = 20 m

Thus maximum height, H, is :

H = H 1 + H 2 = 20 + 160 = 180 m

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Projectile thrown down at an angle with horizontal direction

Projectile motion here is similar to that of projectile thrown horizontally. The only difference is that the projectile has a finite component of velocity in downward direction against zero vertical velocity.

For convenience, the point of projection is considered as origin of reference and the positive x and y directions of the coordinate system are considered in horizontal and vertically downward directions.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
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Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
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da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
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Alexandre
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Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
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LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
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
Smarajit Reply
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Source:  OpenStax, Kinematics fundamentals. OpenStax CNX. Sep 28, 2008 Download for free at http://cnx.org/content/col10348/1.29
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