FUND.OF PHYSICS (LL)
12th Edition
ISBN: 9781119801146
Author: Halliday
Publisher: WILEY
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Chapter 4, Problem 81P
(a)
To determine
To find: Velocity of A relative to B in unit vector notation along East direction.
(b)
To determine
To find: The position of A relative to B with respect to time.
(c)
To determine
To find: The time at which there is least separation between the ships.
(d)
To determine
To find: The least separation between the ships.
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Question 3 of 17
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In the figure above, three uniform thin rods, each of length L, form
an inverted U. The vertical rods each have a mass m; the horizontal
rod has a mass 3m.
NOTE: Express your answer in terms of the variables given.
(a) What is the x coordinate of the system's center of mass?
xcom
L
2
(b) What is the y coordinate of the system's center of mass?
Ycom
45
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Sketch the harmonic on graphing paper.
Exercise 1:
(a) Using the explicit formulae derived in the lectures for the (2j+1) × (2j + 1) repre-
sentation matrices Dm'm, (J/h), derive the 3 × 3 matrices corresponding to the case
j = 1.
(b) Verify that they satisfy the so(3) Lie algebra commutation relation:
[D(Î₁/ħ), D(Î₂/h)]m'm₁ = iƊm'm² (Ĵ3/h).
(c) Prove the identity
3
Dm'm,(β) = Σ (D(Ρ)D(Ρ))m'¡m; ·
i=1
Chapter 4 Solutions
FUND.OF PHYSICS (LL)
Ch. 4 - When Paris was shelled from 100 km away with the...Ch. 4 - You are to launch a rocket, from just above the...Ch. 4 - An airplane flying horizontally at a constant...Ch. 4 - a Is it possible to be accelerating while...Ch. 4 - While riding in a moving car, you toss an egg...Ch. 4 - A snowball is thrown from ground level by someone...Ch. 4 - You are driving directly behind a pickup truck,...Ch. 4 - At what point in the path of a projectile is the...Ch. 4 - In shot put, the shot is put thrown from above the...Ch. 4 - Prob. 1P
Ch. 4 - A watermelon seed has the following coordinates: x...Ch. 4 - A positron undergoes a displacement r = 2.0 i 3.0...Ch. 4 - The minute hand of a wall clock measures 10 cm...Ch. 4 - SSM A train at a constant 60.0 km/h moves east for...Ch. 4 - An electrons position is given by...Ch. 4 - An ions position vector is initially...Ch. 4 - A plane flies 483 km east from city A to city B in...Ch. 4 - Prob. 11PCh. 4 - At one instant a bicyclist is 40.0 m due east of a...Ch. 4 - SSM A particle moves so that its position in...Ch. 4 - A proton initially has v=4.0i2.0j+3.0k and then...Ch. 4 - SSM ILW A particle leaves the origin with an...Ch. 4 - GO The velocity v of a particle moving in the xy...Ch. 4 - A cart is propelled over an xy plane with...Ch. 4 - A moderate wind accelerates a pebble over a...Ch. 4 - The acceleration of a particle moving only on a...Ch. 4 - A dart is thrown horizontally with an initial...Ch. 4 - A small ball rolls horizontally off the edge of a...Ch. 4 - A projectile is fired horizontally from a gun that...Ch. 4 - In the 1991 World Track and Field Championships in...Ch. 4 - The current world-record motorcycle jump is 77.0...Ch. 4 - A stone is catapulted at time t = 0, with an...Ch. 4 - A projectiles launch speed is five times its speed...Ch. 4 - GO A soccer ball is kicked from the ground with an...Ch. 4 - In a jump spike, a volleyball player slams the...Ch. 4 - SSM A plane, diving with constant speed at an...Ch. 4 - A trebuchet was a hurling machine built to attack...Ch. 4 - SSM A rifle that shoots bullets at 460 m/s is to...Ch. 4 - GO During a tennis match, a player serves the ball...Ch. 4 - SSM WWW A lowly high diver pushes off horizontally...Ch. 4 - Suppose that a shot putter can put a shot at the...Ch. 4 - ILW A ball is shot from the ground into the air....Ch. 4 - A baseball leaves a pitchers hand horizontally at...Ch. 4 - GO In basketball, hang is an illusion in which a...Ch. 4 - Prob. 47PCh. 4 - SSM A football kicker can give the ball an initial...Ch. 4 - GO Two seconds after being projected from ground...Ch. 4 - SSM A ball rolls horizontally off the top of a...Ch. 4 - An Earth satellite moves in a circular orbit 640...Ch. 4 - A carnival merry-go-round rotates about a vertical...Ch. 4 - A rotating fan completes 1200 revolutions every...Ch. 4 - ILW A woman rides a carnival Ferris wheel at...Ch. 4 - A centripetal-acceleration addict rides in uniform...Ch. 4 - When a large star becomes a supernova, its core...Ch. 4 - What is the magnitude of the acceleration of a...Ch. 4 - GO At t1 = 2.00 s, the acceleration of a particle...Ch. 4 - GO A particle moves horizontally in uniform...Ch. 4 - A purse at radius 2.00 m and a wallet at radius...Ch. 4 - A particle moves along a circular path over a...Ch. 4 - SSM WWW A boy whirls a stone in a horizontal...Ch. 4 - GO A cat rides a merry-go-round turning with...Ch. 4 - A cameraman on a pickup truck is traveling...Ch. 4 - A boat is traveling upstream in the positive...Ch. 4 - A suspicious-looking man runs as fast as he can...Ch. 4 - A rugby player runs with the ball directly toward...Ch. 4 - After flying for 15 min in a wind blowing 42 km/h...Ch. 4 - SSM A train travels due south at 30 m/s relative...Ch. 4 - A light plane attains an airspeed of 500 km/h. The...Ch. 4 - SSM Snow is falling vertically at a constant speed...Ch. 4 - SSM ILW Two ships, A and B, leave port at the same...Ch. 4 - GO A 200-m-wide river flows due east at a uniform...Ch. 4 - Prob. 81PCh. 4 - GO A 200-m-wide river has a uniform flow speed of...Ch. 4 - Prob. 83PCh. 4 - You are kidnapped by political-science majors who...Ch. 4 - SSM A baseball is hit at ground level. The ball...Ch. 4 - Long flights at midlatitudes in the Northern...Ch. 4 - SSM A particle starts from the origin at t = 0...Ch. 4 - An astronaut is rotated in a horizontal centrifuge...Ch. 4 - SSM Oasis A is 90 km due west of oasis B. A desert...Ch. 4 - For womens volleyball the top of the net is 2.24 m...Ch. 4 - SSM A rifle is aimed horizontally at a target 30 m...Ch. 4 - A particle is in uniform circular motion about the...Ch. 4 - An iceboat sails across the surface of a frozen...Ch. 4 - Prob. 101PCh. 4 - A magnetic field forces an electron to move in a...Ch. 4 - In 3.50 h, a balloon drifts 21.5 km north, 9.70 km...Ch. 4 - A ball is thrown horizontally from a height of 20...Ch. 4 - A projectile is launched with an initial speed of...Ch. 4 - The position vector for a proton is initially...Ch. 4 - The fast French train known as the TGV Train ...Ch. 4 - a If an electron is projected horizontally with a...Ch. 4 - A person walks up a stalled 15-m-long escalator in...Ch. 4 - a What is the magnitude of the centripetal...Ch. 4 - The range of a projectile depends not only on v0...Ch. 4 - The position vector r of a particle moving in the...Ch. 4 - Prob. 115PCh. 4 - Prob. 116PCh. 4 - Prob. 117PCh. 4 - Prob. 118PCh. 4 - Prob. 119PCh. 4 - Prob. 120PCh. 4 - Prob. 121PCh. 4 - Prob. 122PCh. 4 - Prob. 123PCh. 4 - Prob. 124PCh. 4 - Prob. 125PCh. 4 - Prob. 126PCh. 4 - Prob. 127PCh. 4 - Prob. 128P
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