# 9.7 Rocket propulsion  (Page 7/8)

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Two billiard balls are at rest and touching each other on a pool table. The cue ball travels at 3.8 m/s along the line of symmetry between these balls and strikes them simultaneously. If the collision is elastic, what is the velocity of the three balls after the collision?

final velocity of cue ball is $\text{−}\left(0.76\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{i}$ , final velocities of the other two balls are 2.6 m/s at ±30° with respect to the initial velocity of the cue ball

A billiard ball traveling at $\left(2.2\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{i}-\left(0.4\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{j}$ collides with a wall that is aligned in the $\stackrel{^}{j}$ direction. Assuming the collision is elastic, what is the final velocity of the ball?

Two identical billiard balls collide. The first one is initially traveling at $\left(2.2\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{i}-\left(0.4\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{j}$ and the second one at $\text{−}\left(1.4\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{i}+\left(2.4\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{j}$ . Suppose they collide when the center of ball 1 is at the origin and the center of ball 2 is at the point $\left(2R,0\right)$ where R is the radius of the balls. What is the final velocity of each ball?

ball 1: $\text{−}\left(1.4\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{i}-\left(0.4\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{j}$ , ball 2: $\left(2.2\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{i}+\left(2.4\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{j}$

Repeat the preceding problem if the balls collide when the center of ball 1 is at the origin and the center of ball 2 is at the point $\left(0,2R\right)$ .

Repeat the preceding problem if the balls collide when the center of ball 1 is at the origin and the center of ball 2 is at the point $\left(\sqrt{3}R\text{/}2,R\text{/}2\right)$

ball 1: $\left(1.4\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{i}-\left(1.7\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{j}$ , ball 2: $\text{−}\left(2.8\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{i}+\left(0.012\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{j}$

Where is the center of mass of a semicircular wire of radius R that is centered on the origin, begins and ends on the x axis, and lies in the x , y plane?

Where is the center of mass of a slice of pizza that was cut into eight equal slices? Assume the origin is at the apex of the slice and measure angles with respect to an edge of the slice. The radius of the pizza is R .

$\left(r,\theta \right)=\left(2R\text{/}3,\pi \text{/}8\right)$

If the entire population of Earth were transferred to the Moon, how far would the center of mass of the Earth-Moon-population system move? Assume the population is 7 billion, the average human has a mass of 65 kg, and that the population is evenly distributed over both the Earth and the Moon. The mass of the Earth is $5.97\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{24}\text{kg}$ and that of the Moon is $7.34\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{22}\text{kg}$ . The radius of the Moon’s orbit is about $3.84\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}\text{m}$ .

You friend wonders how a rocket continues to climb into the sky once it is sufficiently high above the surface of Earth so that its expelled gasses no longer push on the surface. How do you respond?

Answers may vary. The rocket is propelled forward not by the gasses pushing against the surface of Earth, but by conservation of momentum. The momentum of the gas being expelled out the back of the rocket must be compensated by an increase in the forward momentum of the rocket.

To increase the acceleration of a rocket, should you throw rocks out of the front window of the rocket or out of the back window?

## Challenge

A 65-kg person jumps from the first floor window of a burning building and lands almost vertically on the ground with a horizontal velocity of 3 m/s and vertical velocity of $-9\phantom{\rule{0.2em}{0ex}}\text{m/s}$ . Upon impact with the ground he is brought to rest in a short time. The force experienced by his feet depends on whether he keeps his knees stiff or bends them. Find the force on his feet in each case.

1. First find the impulse on the person from the impact on the ground. Calculate both its magnitude and direction.
2. Find the average force on the feet if the person keeps his leg stiff and straight and his center of mass drops by only 1 cm vertically and 1 cm horizontally during the impact.
3. Find the average force on the feet if the person bends his legs throughout the impact so that his center of mass drops by 50 cm vertically and 5 cm horizontally during the impact.
4. Compare the results of part (b) and (c), and draw conclusions about which way is better.

You will need to find the time the impact lasts by making reasonable assumptions about the deceleration. Although the force is not constant during the impact, working with constant average force for this problem is acceptable.

a. $617\phantom{\rule{0.2em}{0ex}}\text{N}·\text{s}$ , 108°; b. ${F}_{x}=2.91\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}\phantom{\rule{0.2em}{0ex}}\text{N}$ , ${F}_{y}=2.6\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}\phantom{\rule{0.2em}{0ex}}\text{N}$ ; c. ${F}_{x}=5265\phantom{\rule{0.2em}{0ex}}\text{N}$ , ${F}_{y}=5850\phantom{\rule{0.2em}{0ex}}\text{N}$

Two projectiles of mass ${m}_{1}$ and ${m}_{2}$ are ﬁred at the same speed but in opposite directions from two launch sites separated by a distance D . They both reach the same spot in their highest point and strike there. As a result of the impact they stick together and move as a single body afterwards. Find the place they will land.

Two identical objects (such as billiard balls) have a one-dimensional collision in which one is initially motionless. After the collision, the moving object is stationary and the other moves with the same speed as the other originally had. Show that both momentum and kinetic energy are conserved.

Conservation of momentum demands ${m}_{1}{v}_{\text{1,i}}+{m}_{2}{v}_{\text{2,i}}={m}_{1}{v}_{\text{1,f}}+{m}_{2}{v}_{\text{2,f}}$ . We are given that ${m}_{1}={m}_{2}$ , ${v}_{\text{1,i}}={v}_{\text{2,f}}$ , and ${v}_{\text{2,i}}={v}_{\text{1,f}}=0$ . Combining these equations with the equation given by conservation of momentum gives ${v}_{\text{1,i}}={v}_{\text{1,i}}$ , which is true, so conservation of momentum is satisfied. Conservation of energy demands $\frac{1}{2}{m}_{1}{v}_{\text{1,i}}^{2}+\frac{1}{2}{m}_{2}{v}_{\text{2,i}}^{2}=\frac{1}{2}{m}_{1}{v}_{\text{1,f}}^{2}+\frac{1}{2}{m}_{2}{v}_{\text{2,f}}^{2}$ . Again combining this equation with the conditions given above give ${v}_{\text{1,i}}={v}_{\text{1,i}}$ , so conservation of energy is satisfied.

A ramp of mass M is at rest on a horizontal surface. A small cart of mass m is placed at the top of the ramp and released.

What are the velocities of the ramp and the cart relative to the ground at the instant the cart leaves the ramp?

Find the center of mass of the structure given in the figure below. Assume a uniform thickness of 20 cm, and a uniform density of $1{\phantom{\rule{0.2em}{0ex}}\text{g/cm}}^{3}.$

Assume origin on centerline and at floor, then $\left({x}_{\text{CM}},{y}_{\text{CM}}\right)=\left(0,86\phantom{\rule{0.2em}{0ex}}\text{cm}\right)$

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
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
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
jyotirmayee
Nirupam
its fine,,most welcome
jyotirmayee
what is three dimensional coordinate system?
considering the change of vectors in all three dimensions of space
vedanth
direction co-sign of vector questions
opposite
Sonu
opposite mean
Vipin
what is the different between action and reaction?
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
or we can say , reaction is the result of action
Ritik