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x = R = u x T = u 2 H g

Problem : A plane flying at the speed of 100 m/s parallel to the ground drops an object from a height of 2 km. Find (i) the time of flight (ii) velocity of the object at the time it strikes the ground and (iii) the horizontal distance traveled by the object.

Solution : The basic approach to solve the problem involves consideration of motion in two mutually perpendicular direction. Here, we consider a coordinate system with the point of release as the origin and down ward direction as the positive y-direction.

An object dropped from a plane moving in horizontal direction

(i) Time of flight, T

In vertical direction :

u y = 0 , a = 10 m / s 2 , y = 2000 m , T = ?

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

y = 1 2 g t 2 T = ( 2 y g ) T = ( 2 x 2000 10 ) = 20 s

(ii) Velocity at the ground

We can find the velocity at the time of strike with ground by calculating component velocities at that instant in the two mutually perpendicular directions and finding the resultant (composite) velocity as :

v = ( v x 2 + v y 2 )

Initial vertical component of initial velocity (uy) is zero and the object is accelerated down with the acceleration due to gravity. Hence,

v y = u y + g t = 0 + g t = g t

The component of velocity in the horizontal direction remains unchanged as there is no acceleration in this direction.

v x = u x = u

v = ( v x 2 + v y 2 ) = ( u 2 + g 2 t 2 )

Putting values,

v = ( 100 2 + 10 2 x 20 2 ) = 50000 = 100 5 m / s

(iii) Horizontal distance traveled

From consideration of uniform motion in horizontal direction, we have :

x = u x t = u t

Putting values,

x = R = 100 x 20 = 2000 m

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A ball is thrown horizontally from a tower at a speed of 40 m/s. The speed of the projectile (in m/s) after 3 seconds, before it touches the ground, is (consider g = 10 m / s 2 ) :

a 30 b 40 c 50 d 60

Here, we consider a reference system whose origin coincides with the point of projection. The downward direction is along y - direction as shown in the figure.

Projectile motion

Projectile motion

The initial speed of the projectile is equal to the horizontal component of the velocity, which remains unaltered during projectile motion. On the other hand, vertical component of velocity at the start of motion is zero. Thus,

u x = 40 m / s , u y = 0

Using equation of motion, we have :

v y = u y + a y t v y = 0 + g t = 10 X 3 = 30 m / s

Since the horizontal component of velocity remains unaltered, the speed, after 3 second, is :

v = v x 2 + v y 2 = 40 2 + 30 2 = 50 m / s Hence, option (c) is correct.

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A ball is projected horizontally from a height at a speed of 30 m/s. The time after which the vertical component of velocity becomes equal to horizontal component of velocity is : (consider g = 10 m / s 2 ) :

a 1 s b 2 s c 3 s d 4 s

The ball does not have vertical component of velocity when projected. The ball, however, is accelerated downward and gains speed in vertical direction. At certain point of time, the vertical component of velocity equals horizontal component of velocity. At this instant, the angle that the velocity makes with the horizontal is :

Projectile motion

Projectile motion

tan θ = v y v x = 1 θ = 45 0

We should note that this particular angle of 45° at any point during the motion, as a matter of fact, signifies that two mutually perpendicular components are equal.

But we know that horizontal component of velocity does not change during the motion. It means that vertical component of velocity at this instant is equal to horizontal component of velocity i.e.

v y = v x = u x = 30 m / s

Further, we know that we need to analyze motion in vertical direction to find time as required,

v y = u y + a y t 30 = 0 + 10 t t = 3 s

Hence, option (c) is correct.

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Questions & Answers

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
what is the stm
Brian Reply
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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
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How we are making nano material?
LITNING Reply
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LITNING
scanning tunneling microscope
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
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what is differents between GO and RGO?
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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
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
anyone know any internet site where one can find nanotechnology papers?
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research.net
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sciencedirect big data base
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Introduction about quantum dots in nanotechnology
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what does nano mean?
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nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
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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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