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  1. From [link] , v 2 = v 0 2 2 g ( y y 0 ) . With v = 0 and y 0 = 0 , we can solve for y :
    y = v 0 2 −2 g = ( 2.0 × 10 2 m / s ) 2 −2 ( 9.8 m / s 2 ) = 2040.8 m .

    This solution gives the maximum height of the booster in our coordinate system, which has its origin at the point of release, so the maximum height of the booster is roughly 7.0 km.
  2. An altitude of 6.0 km corresponds to y = 1.0 × 10 3 m in the coordinate system we are using. The other initial conditions are y 0 = 0 , and v 0 = 200.0 m/s .
    We have, from [link] ,
    v 2 = ( 200.0 m / s ) 2 2 ( 9.8 m / s 2 ) ( 1.0 × 10 3 m ) v = ± 142.8 m / s .


We have both a positive and negative solution in (b). Since our coordinate system has the positive direction upward, the +142.8 m/s corresponds to a positive upward velocity at 6000 m during the upward leg of the trajectory of the booster. The value v = −142.8 m/s corresponds to the velocity at 6000 m on the downward leg. This example is also important in that an object is given an initial velocity at the origin of our coordinate system, but the origin is at an altitude above the surface of Earth, which must be taken into account when forming the solution.

Visit this site to learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (for example, y = bx ) to see how they add to generate the polynomial curve.


  • An object in free fall experiences constant acceleration if air resistance is negligible.
  • On Earth, all free-falling objects have an acceleration g due to gravity, which averages g = 9.81 m/s 2 .
  • For objects in free fall, the upward direction is normally taken as positive for displacement, velocity, and acceleration.

Conceptual questions

What is the acceleration of a rock thrown straight upward on the way up? At the top of its flight? On the way down? Assume there is no air resistance.

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An object that is thrown straight up falls back to Earth. This is one-dimensional motion. (a) When is its velocity zero? (b) Does its velocity change direction? (c) Does the acceleration have the same sign on the way up as on the way down?

a. at the top of its trajectory; b. yes, at the top of its trajectory; c. yes

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Suppose you throw a rock nearly straight up at a coconut in a palm tree and the rock just misses the coconut on the way up but hits the coconut on the way down. Neglecting air resistance and the slight horizontal variation in motion to account for the hit and miss of the coconut, how does the speed of the rock when it hits the coconut on the way down compare with what it would have been if it had hit the coconut on the way up? Is it more likely to dislodge the coconut on the way up or down? Explain.

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The severity of a fall depends on your speed when you strike the ground. All factors but the acceleration from gravity being the same, how many times higher could a safe fall on the Moon than on Earth (gravitational acceleration on the Moon is about one-sixth that of the Earth)?

Earth v = v 0 g t = g t ; Moon v = g 6 t v = v g t = g 6 t t = 6 t ; Earth y = 1 2 g t 2 Moon y = 1 2 g 6 ( 6 t ) 2 = 1 2 g 6 t 2 = −6 ( 1 2 g t 2 ) = −6 y

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How many times higher could an astronaut jump on the Moon than on Earth if her takeoff speed is the same in both locations (gravitational acceleration on the Moon is about on-sixth of that on Earth)?

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Questions & Answers

what is wave
Alfred Reply
who can state the third equation of motion
two particles rotate in a rigid body then acceleration will be ?
kinza Reply
same acceleration for all particles because all prticles will be moving with same angular velocity.so at any time interval u find same acceleration of all the prticles
what is electromagnetism
David Reply
It is the study of the electromagnetic force, one of the four fundamental forces of nature. ... It includes the electric force, which pushes all charged particles, and the magnetic force, which only pushes moving charges.
what is units?
Subhajit Reply
units as in how
What is th formular for force
Joseph Reply
F = m x a
State newton's second law of motion
Seth Reply
can u tell me I cant remember
force is equal to mass times acceleration
The acceleration of a system is directly proportional to the and in the same direction as the external force acting on the system and inversely proportional to its mass that is f=ma
The uniform seesaw shown below is balanced on a fulcrum located 3.0 m from the left end. The smaller boy on the right has a mass of 40 kg and the bigger boy on the left has a mass 80 kg. What is the mass of the board?
Asad Reply
Consider a wave produced on a stretched spring by holding one end and shaking it up and down. Does the wavelength depend on the distance you move your hand up and down?
Sohail Reply
no, only the frequency and the material of the spring
how to read physics ncert?
beat line read important. line under line
how can one calculate the value of a given quantity
Helen Reply
To determine the exact value of a percent of a given quantity we need to express the given percent as fraction and multiply it by the given number.
briefly discuss rocket in physics
Ibrahim Reply
ok let's discuss
What is physics
Nura Reply
physics is the study of natural phenomena with concern with matter and energy and relationships between them
a potential difference of 10.0v is connected across a 1.0AuF in an LC circuit. calculate the inductance of the inductor that should be connected to the capacitor for the circuit to oscillate at 1125Hza potential difference of 10.0v is connected across a 1.0AuF in an LC circuit. calculate the inducta
Royalty Reply
L= 0.002H
how did you get it?
is the magnetic field of earth changing
tibebeab Reply
what is thought to be the energy density of multiverse and is the space between universes really space
can you explain it
Energy can not either created nor destroyed .therefore who created? and how did it come to existence?
Suzana Reply
this greatly depend on the kind of energy. for gravitational energy, it is result of the shattering effect violent collision of two black holes on the space-time which caused space time to be disturbed. this is according to recent study on gravitons and gravitational ripple. and many other studies
and not every thing have to pop into existence. and it could have always been there . and some scientists think that energy might have been the only entity in the euclidean(imaginary time T=it) which is time undergone wick rotation.
What is projectile?
Nana Reply
An object that is launched from a device
2 dimensional motion under constant acceleration due to gravity
Not always 2D Awais
no comments
why not? a bullet is a projectile, so is a rock I throw
bullet travel in x and y comment same as rock which is 2 dimensional
no all pf you are wrong. projectile is any object propelled through space by excretion of a force which cease after launch
for awais, there is no such thing as constant acceleration due to gravity, because gravity change from place to place and from different height
it is the object not the motion or its components
Practice Key Terms 2

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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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