# 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 $\left({x}_{\text{CM}},{y}_{\text{CM}}\right)=\left(0,86\phantom{\rule{0.2em}{0ex}}\text{cm}\right)$

lists 5 drawing instruments and their uses
that is a question you can find on Google, anyway of top of my head, compass, ruler, protractor, try square, triangles.
Rongfang
A force F is needed to break a copper wire having radius R. The force needed to break a copper wire of radius 2R will be
2F
Jacob
The difference between vector and scaler quantity
vector has both magnitude & direction but scalar has only magnitude
Manash
my marunong ba dto mag prove ng geometry
ron
how do I find resultant of four forces at a point
Inusah
use the socatoa rule
kingsley
draw force diagram, then work out the direction of force.
Rongfang
In a closed system of forces... Summation of forces in any direction or plane is zero... Resolve if there is a need to then add forces in a particular plane or direction.. Say the x direction... Equate it tk zero
Jacob
define moment of inertia
it is the tendency for a body to continue in motion if is or continue to be at rest if it is.
prince
what is Euler s theorem
what is thermocouple?
joining of two wire of different material forming two junctions. If one is hot and another is cold the it will produce emf...
joining of two metal of different materials to form a junction in one is hot & another is cold
Manash
define dimensional analysis
mathematical derivation?
Hira
explain what Newtonian mechanics is.
a system of mechanics based of Newton laws motion this is easy difenation of mean...
Arzoodan
what is the meaning of single term,mechanics?
jyotirmayee
mechanics is the science related to the behavior of physical bodies when some external force is applied to them
Lalita
SO ASK What is Newtonian mechanics in physics? Newtonian physics, also calledNewtonian or classical mechanics, is the description of mechanical events—those that involve forces acting on matter—using the laws of motion and gravitation formulated in the late seventeenth century by English physicist
Suleiman
can any one send me the best reference book for physics?
Prema
concept of physics by HC verma, Fundamentals of Physics, university of physics
tq u.
Prema
these are the best physics books one can fond both theory and applications.
can any one suggest best book for maths with lot of Tricks?
Vivek
what is the water height in barometer?
SUNEELL
13.5*76 cm. because Mercury is 13.5 times dense than Mercury
LOVE
water is 13.5 times dense than the Mercury
LOVE
plz tell me frnds the best reference book for physics along with the names of authors.
Prema
i recomended the reference book for physics from library University of Dublin or library Trinity college
Arzoodan
A little help here... . 1. Newton's laws of Motion, are they applicable to motions of all speeds? 2.state the speeds which are applicable to Newtons laws of Motion
Derek
mechanics which follows Newtons law
Manash
The definition of axial and polar vector .
Arpita
polar vector which have a starting point or pt. of applications is,force,displacement
jyotirmayee
axial vector represent rotational effect and act along the axis of rotation b
jyotirmayee
prove Newton's first law of motion
prince
explain the rule of free body diagram
The polar coordinates of a point are 4π/3 and 5.50m. What are its Cartesian coordinates?
application of elasticity
good
Anwar
a boy move with a velocity of 5m/s in 4s. What is the distance covered by the boy?
What is the time required for the sun to reach the earth?
anthony
24th hr's, your question is amazing joke 😂
Arzoodan
velocity 20 m, s
Ahmed
the sun shines always and the earth rotates so the question should specify a place on earth and that will be 24hrs
Opoku
20m
Gabriel
good nice work
Anwar
20m
Evelyn
why 20?.
Arzoodan
v =distance/time so make distance the subject from the equation
Evelyn
20m
Olaide
exatly
Arzoodan
what is differemce between principles and laws
plz
Anwar
how can a 50W light bulb use more energy than a 1000W oven?
That depends on how much time we use them
Phrangsngi
It states that, " If two vectors are represented in magnitude and direction by the two sides of a triangle, then their resultant is represented in magnitude and direction by the third side of the triangl " .
Nabin
thanks yaar
Pawan
And it's formula
Pawan
Manash