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Solution

1. Identify the knowns. y 0 = 0 ; y 1 = 5 . 10 m ; v 0 = 13 .0 m/s ; a = g = 9 . 80 m /s 2 size 12{a= - g= - 9 "." "80"" m/s" rSup { size 8{2} } } {} .

2. Choose the kinematic equation that makes it easiest to solve the problem. The equation v 2 = v 0 2 + 2 a ( y y 0 ) works well because the only unknown in it is v . (We will plug y 1 in for y .)

3. Enter the known values

v 2 = 13 . 0 m/s 2 + 2 9 . 80 m/s 2 5 . 10 m 0 m = 268 . 96 m 2 /s 2 , size 12{v rSup { size 8{2} } = left ( - "13" "." "0 m/s" right ) rSup { size 8{2} } +2 left ( - 9 "." "80 m/s" rSup { size 8{2} } right ) left ( - 5 "." "10 m" - "0 m" right )="268" "." "96 m" rSup { size 8{2} } "/s" rSup { size 8{2} } } {}

where we have retained extra significant figures because this is an intermediate result.

Taking the square root, and noting that a square root can be positive or negative, gives

v = ± 16 .4 m/s .

The negative root is chosen to indicate that the rock is still heading down. Thus,

v = 16 .4 m/s . size 12{v= - "16" "." 4`"m/s"} {}

Discussion

Note that this is exactly the same velocity the rock had at this position when it was thrown straight upward with the same initial speed . (See [link] and [link] (a).) This is not a coincidental result. Because we only consider the acceleration due to gravity in this problem, the speed of a falling object depends only on its initial speed and its vertical position relative to the starting point. For example, if the velocity of the rock is calculated at a height of 8.10 m above the starting point (using the method from [link] ) when the initial velocity is 13.0 m/s straight up, a result of ± 3 . 20 m/s size 12{ +- 3 "." "20"`"m/s"} {} is obtained. Here both signs are meaningful; the positive value occurs when the rock is at 8.10 m and heading up, and the negative value occurs when the rock is at 8.10 m and heading back down. It has the same speed but the opposite direction.

Two figures are shown. At left, a man standing on the edge of a cliff throws a rock straight up with an initial speed of thirteen meters per second. At right, the man throws the rock straight down with a speed of thirteen meters per second. In both figures, a line indicates the rock’s trajectory. When the rock is thrown straight up, it has a speed of minus sixteen point four meters per second at minus five point one zero meters below the point where the man released the rock. When the rock is thrown straight down, the velocity is the same at this position.
(a) A person throws a rock straight up, as explored in [link] . The arrows are velocity vectors at 0, 1.00, 2.00, and 3.00 s. (b) A person throws a rock straight down from a cliff with the same initial speed as before, as in [link] . Note that at the same distance below the point of release, the rock has the same velocity in both cases.

Another way to look at it is this: In [link] , the rock is thrown up with an initial velocity of 13 .0 m/s . It rises and then falls back down. When its position is y = 0 on its way back down, its velocity is 13 .0 m/s . That is, it has the same speed on its way down as on its way up. We would then expect its velocity at a position of y = 5 . 10 m to be the same whether we have thrown it upwards at + 13 .0 m/s or thrown it downwards at 13 .0 m/s . The velocity of the rock on its way down from y = 0 is the same whether we have thrown it up or down to start with, as long as the speed with which it was initially thrown is the same.

Find g From data on a falling object

The acceleration due to gravity on Earth differs slightly from place to place, depending on topography (e.g., whether you are on a hill or in a valley) and subsurface geology (whether there is dense rock like iron ore as opposed to light rock like salt beneath you.) The precise acceleration due to gravity can be calculated from data taken in an introductory physics laboratory course. An object, usually a metal ball for which air resistance is negligible, is dropped and the time it takes to fall a known distance is measured. See, for example, [link] . Very precise results can be produced with this method if sufficient care is taken in measuring the distance fallen and the elapsed time.

Questions & Answers

hello friends what is hadronic heating systems
Rabilu Reply
Hydronics is the use of a liquid heat-transfer medium in heating and cooling systems. 
Balogun
what is mass
Victor Reply
is the amount of an object
Sendawula
mass is the measure of the inertia of a body
Ishmeal
advantages of CRO over ordinary voltmeter
Dismas Reply
what is the difference between displacement and distance?!
Daniel Reply
what is equilibrium
Sade Reply
If a system is said to be under equilibrium whenever there is no force act upon it... And it remain in its initial stage..
soniya
what is velocity
Ahmed
time rate of displacement of a body is called velocity
muhammad
velocity is the gradient of acceleration time graph
Etana
actually equilibrium is when a body is in total balance where in no external force is acting on it. Or the forces on the left hand side equal those on the left hand side and downward forces equal upward forces & anticlockwise moment equal clockwise moment about the same point.
Etana
I mean left hand side and right hand side
Etana
What is conductivity
Saud Reply
It is the ease with which electrical charges or heat can be transmitted through a material or a solution.
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how to find magnitude and direction
Arjune Reply
how to caclculate for speed
Arjune
derivation of ohms law
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derivation of resistance
Kazeem
R=v/I where R=resistor, v=voltage, I=current
Kazeem
magnitude
Arjune
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Arjune
Electric current is the flow of electrons
Kelly Reply
is there really flow of electrons exist?
babar
Yes It exists
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babar
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babar
an electron will flow accross a conductor because or when it posseses kinectic energy
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electron can not flow jist trasmit electrical energy
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free electrons of conductor
ankita
electric means the flow heat current.
Serah Reply
electric means the flow of heat current in a circuit.
Serah
What is electric
Manasseh Reply
electric means?
ghulam
electric means the flow of heat current in a circuit.
Serah
electric means the flow of electric current through conductor
Sade
the continuos flow of electrons in a circuit is called electric
ANUBHA
electric means charge
ghulam
electric means current
Sade
flow of current.
Sendawula
a boy cycles continuously through a distance of 1.0km in 5minutes. calculate his average speed in ms-1(meter per second). how do I solve this
Jenny Reply
speed = distance/time be sure to convert the km to m and minutes to seconds check my utube video "mathwithmrv speed"
PhysicswithMrV
d=1.0km÷1000=0.001 t=5×60=300s s=d\t s=0.001/300=0.0000033m\s
Serah
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Arjune
D=1km=1000m t=5mins×60secs=300sec s=d/t=3.333m/s
Daniel
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Amalia
why we cannot use DC instead of AC in a transformer
kusshaf Reply
becuse the d .c cannot travel for long distance trnsmission
ghulam
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Chiwetalu Reply
branch of science which deals with matter energy and their relationship between them
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Life science
the
what is heat and temperature
Kazeem Reply
Practice Key Terms 2

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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