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Check Your Understanding If the two golf shots in [link] were launched at the same speed, which shot would have the greatest range?

The golf shot at 30 ° .

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When we speak of the range of a projectile on level ground, we assume R is very small compared with the circumference of Earth. If, however, the range is large, Earth curves away below the projectile and the acceleration resulting from gravity changes direction along the path. The range is larger than predicted by the range equation given earlier because the projectile has farther to fall than it would on level ground, as shown in [link] , which is based on a drawing in Newton’s Principia . If the initial speed is great enough, the projectile goes into orbit. Earth’s surface drops 5 m every 8000 m. In 1 s an object falls 5 m without air resistance. Thus, if an object is given a horizontal velocity of 8000 m / s (or 18,000 mi / hr ) near Earth’s surface, it will go into orbit around the planet because the surface continuously falls away from the object. This is roughly the speed of the Space Shuttle in a low Earth orbit when it was operational, or any satellite in a low Earth orbit. These and other aspects of orbital motion, such as Earth’s rotation, are covered in greater depth in Gravitation .

The figure shows a drawing of the earth with a tall tower at the north pole and a horizontal arrow labeled v 0 pointing to the right. 5 trajectories that start at the top of the tower are shown. The first reaches the earth near the tower. The second reaches the earth farther from the tower, and the third even farther. The fourth trajectory hits the earth at the equator, and is tangent to the surface at the equator. The fifth trajectory is a circle concentric with the earth.
Projectile to satellite. In each case shown here, a projectile is launched from a very high tower to avoid air resistance. With increasing initial speed, the range increases and becomes longer than it would be on level ground because Earth curves away beneath its path. With a speed of 8000 m/s, orbit is achieved.

At PhET Explorations: Projectile Motion , learn about projectile motion in terms of the launch angle and initial velocity.

Summary

  • Projectile motion is the motion of an object subject only to the acceleration of gravity, where the acceleration is constant, as near the surface of Earth.
  • To solve projectile motion problems, we analyze the motion of the projectile in the horizontal and vertical directions using the one-dimensional kinematic equations for x and y .
  • The time of flight of a projectile launched with initial vertical velocity v 0 y on an even surface is given by
    T t o f = 2 ( v 0 sin θ ) g .

    This equation is valid only when the projectile lands at the same elevation from which it was launched.
  • The maximum horizontal distance traveled by a projectile is called the range. Again, the equation for range is valid only when the projectile lands at the same elevation from which it was launched.

Conceptual questions

Answer the following questions for projectile motion on level ground assuming negligible air resistance, with the initial angle being neither 0 ° nor 90 ° : (a) Is the velocity ever zero? (b) When is the velocity a minimum? A maximum? (c) Can the velocity ever be the same as the initial velocity at a time other than at t = 0? (d) Can the speed ever be the same as the initial speed at a time other than at t = 0?

a. no; b. minimum at apex of trajectory and maximum at launch and impact; c. no, velocity is a vector; d. yes, where it lands

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Answer the following questions for projectile motion on level ground assuming negligible air resistance, with the initial angle being neither 0 ° nor 90 ° : (a) Is the acceleration ever zero? (b) Is the acceleration ever in the same direction as a component of velocity? (c) Is the acceleration ever opposite in direction to a component of velocity?

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Questions & Answers

what's the working difference between a dynamo and a pump?
Piyali Reply
a dynamo is basically a dc generator while pump is usually equipped with a motor
vedanth
a dynamo converts mechanical energy to electrical while a pump is opposite to that
vedanth
nice
Piyali
why sea water looks bluish?
Piyali Reply
cuz the sky is blue...
Mehdi
you see the reflexion of the "blue" sky in the water
Mehdi
somewhere sea water turns green why?
Piyali
never seen bro... are u sure ?
Mehdi
ur answer was correct but due to the presence of phytoplankton color can be changed near the shore
Piyali
waaaww... you re awesome
Mehdi
i need solutions of unuversity pbysucs volume 1
Vimla Reply
what is three dimensional coordinate system?
Sachindra Reply
considering the change of vectors in all three dimensions of space
vedanth
direction co-sign of vector questions
Vipin Reply
opposite
Sonu
opposite mean
Vipin
what is the different between action and reaction?
Asali Reply
action is external force. Reaction exists because of the external action. Reaction is mostly an internal force
Yoblaze
The difference is said in the word itself. There is no existance of reaction without an application of action. So action occur first then reaction. Reaction may produce in body itself or to other body i.e., it may be internal or external.
Amalesh
what is total energy
Israel Reply
kenetic energy + potential energy + rotational energy
Tony
any body or object can have it ..even in the molecular level
Tony
As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk of diameter 8.50 ± 0.02 cm and thickness 0.050 ± 0.005 cm. Find the average volume of a cookie and the uncertainty in the volume.
Mike Reply
how can proportionality sign can be replaced by = and propotionality constant aznd why?🙄🙄
Yanjeen Reply
because proportionality means linear relationship between the variables involved
Ranjan
When we say to quantities are proportional to each other, what we mean is that the variables maintain a constant ratio to each other.
Ranjan
let us consider an equation y= mx here y and x are variables and m is constant so whenever we divide y by x it maintains constant ratio called m , if m = 1 y=x if m doesn't equal 1 it may be other but for a closed function it is always same I.e the ratio remains constant
krishna
this applying for closed function proportionality sign can be replaced by = followed by a constant multiplier ratio
krishna
considering the propagation of a wave along the x direction on a vibrating string,how can one derive the one dimensional wave equation for the vibrating sting and the speed expression
Tebovanessapi@gmail. Reply
show whether or not the expression v^2= u^2 sin^2 d- 2gs is dimensionally constant
Oyetayo Reply
the period T of a pendulum depends on its mass m, length l and acceleration due to gravity g. using dimensional analysis, derive for T.
Oyetayo
what is physics
Satyabrata Reply
Physics is the tool humans use to understand the properties characteristics and interactions of where they live - the universe. Thus making laws and theories about the universe in a mathematical way derived from empirical results yielded in tons of experiments.
Jomari
This tool, the physics, also enhances their way of thinking. Evolving integrating and enhancing their critical logical rational and philosophical thinking since the greeks fired the first neurons of physics.
Jomari
nice
Satyabrata
Physics is also under the category of Physical Science which deals with the behavior and properties of physical quantities around us.
Angelo
Physical Science is under the category of Physics*... I prefer the most is Theoretical Physics where it deals with the philosophical view of our world.
Jomari
what is unit
Satyabrata Reply
Metric unit
Arzoodan
A unit is what comes after a number that gives a precise detail on what the number means. For example, 10 kilograms, 10 is the number while "kilogram" is the unit.
Angelo
there are also different types of units, but metric is the most widely used. It is called the SI system. Please research this on google.
Angelo
Unit? Bahay yon
Jomari
How did you get the value as Dcd=0.2Dab
ebewele Reply
Why as Dcd=0.2Dab? where are you got this formula?...
Arzoodan
since the distance Dcd=1.2 and the distance Dab=6.0 the ratio 1.2/6.0 gives the equation Dcd=0.2Dab
sunday
Well done.
Arzoodan
how do we add or deduct zero errors from result gotten using vernier calliper?
Aina Reply
how can i understand if the function are odd or even or neither odd or even
hamzaani
I don't get... do you mean positive or negative@hamzaani
Aina
Verner calliper is an old calculator
Antonio
Function is even if f(-x) =f(x)
Antonio
Function is odd if f(-x) = - f(x)
Antonio
Practice Key Terms 4

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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