# 3.5 Free fall  (Page 4/7)

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## Solution

1. From [link] , ${v}^{2}={v}_{0}^{2}-2g\left(y-{y}_{0}\right)$ . With $v=0\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}{y}_{0}=0$ , we can solve for y :
$y=\frac{{v}_{0}^{2}}{-2g}=\frac{\left(2.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{2}\text{m}\text{/}{\text{s}\right)}^{2}}{-2\left(9.8\phantom{\rule{0.2em}{0ex}}\text{m}\text{/}{\text{s}}^{2}\right)}=2040.8\phantom{\rule{0.2em}{0ex}}\text{m}\text{.}$

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 $y=1.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{m}$ in the coordinate system we are using. The other initial conditions are ${y}_{0}=0,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}{v}_{0}=200.0\phantom{\rule{0.2em}{0ex}}\text{m/s}$ .
We have, from [link] ,
${v}^{2}={\left(200.0\phantom{\rule{0.2em}{0ex}}\text{m}\text{/}\text{s}\right)}^{2}-2\left(9.8\phantom{\rule{0.2em}{0ex}}\text{m}\text{/}{\text{s}}^{2}\right)\left(1.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{m}\right)⇒v=±142.8\phantom{\rule{0.2em}{0ex}}\text{m}\text{/}\text{s}.$

## Significance

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.

## Summary

• 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 $g=9.81\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}$ .
• 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.

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

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.

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 $v={v}_{0}-gt=\text{−}gt$ ; Moon ${v}^{\prime }=\frac{g}{6}{t}^{\prime }\phantom{\rule{0.5em}{0ex}}v={v}^{\prime }\phantom{\rule{0.5em}{0ex}}-gt=-\frac{g}{6}{t}^{\prime }\phantom{\rule{0.5em}{0ex}}{t}^{\prime }=6t$ ; Earth $y=-\frac{1}{2}g{t}^{2}$ Moon ${y}^{\prime }=-\frac{1}{2}\phantom{\rule{0.2em}{0ex}}\frac{g}{6}{\left(6t\right)}^{2}=-\frac{1}{2}g6{t}^{2}=-6\left(\frac{1}{2}g{t}^{2}\right)=-6y$

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)?

#### Questions & Answers

Can someone please tell what really happened to planet Pluto
what are the first 20 elements in periodic table.
H,O...
Arzoodan
what happened to the rest now, or have you forgotten?
Ejiba
who discover periodic table?
it wasn't discovered , it was made.and the person who made it was dmitri mendeleev. dobreinier and newland gave their laws before dmitri related periodic table but wasn't successful in their work
Ritik
Nope, numerous number of scientist had actually contributed in the making of periodic table. Dmitri Mendeleev succeeded making all the elements into the right order in accordance to their atomic number.
Dame
what is the Greek name for calcium
Greek word for calcium is asvestio while Latin name is calf meaning lime or limestone
Ejiba
different types of wave
longitudinal and transverse waves
Ravindra
a gun is kept in the state that it cannot move anywhere and the bullet is fired. Then what is the effect on the velocity of bullet and KE of gun ?
want is meant by the term solar system
it refers to the sun and all heavenly bodies revolving around it.
Danie
excatly...for sure
Arzoodan
in addition to Danie's, a solar system is a collection of planets and their moons, asteroids, and other objects bound together by the Star's gravitational force directly or indirectly.
Galiwango
what is meant by total internal reflection
what iw meant by total internal reflection
Akshay
Lorentz force?
jyotirmayee
study fibre optics. .you will get total internal reflection
Siddhansh
wha
jyotirmayee
what is Lorentz force?
jyotirmayee
a ray of light traveling at an angle of incidence greater than critical angle from denser to rarer medium is totally reflected back into the denser medium is called total internal reflaction
Manoj
motion in strat line where is this chapter
motion in straight line is kinematic's part
Ritik
yea
Manoj
this defination isn't correct
Arzoodan
motion in one dimension
Anil
what is Lorentz force?
what is maxwell electromagnetic law?
jyotirmayee
at what angle should the two forces 2p and root 2p acts so that the resultant force is p root 10
what answer fir this
Akshay
what's the working difference between a dynamo and a pump?
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
okay
Friday
why sea water looks bluish?
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
because of the reflection of the sky
Friday
rays coming from the sun consist of all 7 colours ie.VIBGYOR. when the ray strikes surface of water,all colors gets absorbed by it except blue which gets reflected by it.so we find the sea water appearing bluish
Ritik
how can someone identify sea water from rain water
Oniyide
i think it's not possible as because rainwater consists of water from all kind of water bodies ie.lakes,seas etc but u can predict if u have a sea nearby ur home or city
Ritik
i need solutions of unuversity pbysucs volume 1
me too
Nirupam
Help us if anyone knows
Nirupam
bring questions
john
actually if u wanted whole book solution then u should buy the solution book
jyotirmayee
from where
Nirupam
where do u live ,,,,,if u live in Delhi then at bellsarayeiii or from stationary store ,,,,chatarpurrr ,,,,,there is a popular books store,,,,,u have to buy from there
jyotirmayee
Kota Rajasthan
Nirupam
so strange,,,,,r u preparing for pmt,,,?
jyotirmayee
for IIT
Nirupam
then concern near book store
jyotirmayee
in Rajasthan
jyotirmayee
or ask questions here
jyotirmayee
thanks for your help
Nirupam
its fine,,most welcome
jyotirmayee
what is three dimensional coordinate system?
considering the change of vectors in all three dimensions of space
vedanth