Physics (5th Edition)
5th Edition
ISBN: 9780321976444
Author: James S. Walker
Publisher: PEARSON
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Textbook Question
Chapter 4, Problem 8CQ
Two projectiles are launched from the same point at the same angle above the horizontal Projectile 1 reaches a maximum height twice that of projectile 2. What is the ratio of the initial speed of projectile 1 to the initial speed of projectile 2? Explain.
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A conveyor belt at a recycling plant launches bottles and bottle caps into the air, so that an automatic image recognition device can count them. They land at the same height at which they are launched.
Glass bottles are launched at an angle of 35.0° above the horizontal, and land after 0.500s.
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Problem
For a projectile lunched with an initial velocity of v0 at an angle of θ (between 0 and 90o) , a) derive the general expression for maximum height hmax and the horizontal range R. b) For what value of θ gives the highest maximum height?
Solution
The components of v0 are expressed as follows:
vinitial-x = v0cos(θ)
vinitial-y = v0sin(θ)
a)
Let us first find the time it takes for the projectile to reach the maximum height.Using: vfinal-y = vinitial-y + ayt
since the y-axis velocity of the projectile at the maximum height isvfinal-y =___________
Then,
___________= vinitial-y + aytSubstituting the expression of vinitial-y and ay = -g, results to the following:
__________=__________-__________t
Thus, the time to reach the maximum height istmax-height = __________ /__________
We will use this time to the equation
yfinal - yinitial = vinitial-yt + (1/2)ayt2
if we use the time taken to reach the maximum height, therefore, the displacement will yield the maximum height, so
hmax =…
Problem
For a projectile lunched with an initial velocity of v0 at an angle of θ (between 0 and 90o) , a) derive the general expression for maximum height hmax and the horizontal range R. b) For what value of θ gives the highest maximum height?
Solution
The components of v0 are expressed as follows:
vinitial-x = v0cos(θ)
vinitial-y = v0sin(θ)
a)
Let us first find the time it takes for the projectile to reach the maximum height.
Using:
vfinal-y = vinitial-y + ayt
since the y-axis velocity of the projectile at the maximum height is
vfinal-y = ?
Then,
? = vinitial-y + ayt
Substituting the expression of vinitial-y and ay = -g, results to the following:
? = ? - ?t
Thus, the time to reach the maximum height is
tmax-height = ?/?
We will use this time to the equation
yfinal - yinitial = vinitial-yt + (1/2)ayt2
if we use the time taken to reach the maximum height, therefore, the displacement will yield the maximum height, so
hmax = vinitial-yt + (1/2)ayt2
substituting, the vinitial-y…
Chapter 4 Solutions
Physics (5th Edition)
Ch. 4.1 - The equations of motion of an object are x = (1...Ch. 4.2 - A sailor drops a pair of binoculars from the crows...Ch. 4.3 - Two objects, A and B, are launched horizontally,...Ch. 4.4 - A projectile is launched and lands at the same...Ch. 4.5 - A baseball player throws a ball to another player...Ch. 4 - What is the acceleration of a projectile when it...Ch. 4 - A projectile is launched with an initial speed of...Ch. 4 - A projectile is launched from level ground. When...Ch. 4 - In a game of baseball a player hits a high fly...Ch. 4 - A projectile is launched with an initial velocity...
Ch. 4 - A projectile is launched from a level surface with...Ch. 4 - Do projectiles for which air resistance is...Ch. 4 - Two projectiles are launched from the same point...Ch. 4 - A child rides on a pony walking with constant...Ch. 4 - Driving down the highway, you find yourself behind...Ch. 4 - A projectile is launched from the origin of a...Ch. 4 - Predict/Explain As you walk briskly down the...Ch. 4 - A sailboat runs before the wind with a constant...Ch. 4 - As you walk to class with a constant speed of 1.75...Ch. 4 - Starting from rest, a car accelerates at 2.0 m/s2...Ch. 4 - Predict/Calculate A particle passes through the...Ch. 4 - A skateboarder travels on a horizontal surface...Ch. 4 - A hot-air balloon is drifting in level flight due...Ch. 4 - An electron in a cathode-ray tube is traveling...Ch. 4 - Two canoeists start paddling at the same time and...Ch. 4 - Predict/Explain Two divers run horizontally off...Ch. 4 - Predict/Explain Two youngsters dive off an...Ch. 4 - An archer shoots an arrow horizontally at a target...Ch. 4 - Victoria Falls The great, gray-green, greasy...Ch. 4 - A diver runs horizontally off the end of a diving...Ch. 4 - An astronaut on the planet Zircon tosses a rock...Ch. 4 - Predict/Calculate Pitchers Mounds Pitchers mounds...Ch. 4 - Playing shortstop, you pick up a ground ball and...Ch. 4 - Predict/Calculate A crow is flying horizontally...Ch. 4 - A mountain climber jumps a 2.8-m-wide crevasse by...Ch. 4 - Predict/Calculate A white-crowned sparrow flying...Ch. 4 - Pumpkin Toss In Denver, children bring their old...Ch. 4 - Fairgoers ride a Ferris wheel with a radius of...Ch. 4 - Predict/Calculate A swimmer runs horizontally off...Ch. 4 - Baseball and the Washington Monument On August 25,...Ch. 4 - A basketball is thrown horizontally with an...Ch. 4 - Predict/Calculate A ball rolls off a table and...Ch. 4 - A certain projectile is launched with an initial...Ch. 4 - Three projectiles (A, B, and C) are launched with...Ch. 4 - Three projectiles (A, B, and C) are launched with...Ch. 4 - A cannonball is launched at an angle above level...Ch. 4 - A second baseman tosses the ball to the first...Ch. 4 - A soccer ball is kicked with a speed of 15.6 m/s...Ch. 4 - In a game of basketball a forward makes a bounce...Ch. 4 - Predict/Calculate Snowballs are thrown with a...Ch. 4 - In Problem 34, find the direction of motion of the...Ch. 4 - A golfer gives a ball a maximum initial speed of...Ch. 4 - What is the highest tree the ball in the previous...Ch. 4 - The hang time of a punt is measured to be 4.50 s....Ch. 4 - In a friendly game of handball, you hit the ball...Ch. 4 - On a hot summer day a young girl swings on a rope...Ch. 4 - A certain projectile is launched with an initial...Ch. 4 - Punkin Chunkin In Dover, Delaware, a...Ch. 4 - A dolphin jumps with an initial velocity of 12.0...Ch. 4 - A player passes a basketball to another player who...Ch. 4 - A golf ball is struck with a five iron on level...Ch. 4 - Predict/Explain You throw a ball into the air with...Ch. 4 - A football quarterback shows off his skill by...Ch. 4 - A clever inventor has created a device that can...Ch. 4 - Predict/Calculate Volcanoes on lo Astronomers have...Ch. 4 - Predict/Calculate A soccer ball is kicked with an...Ch. 4 - A soccer ball is kicked with an initial speed of...Ch. 4 - An archer shoots an arrow over a castle wall by...Ch. 4 - CE Child 1 throws a snowball horizontally from the...Ch. 4 - CE The penguin to the left in the accompanying...Ch. 4 - CE Dolphins may leap from the water just for the...Ch. 4 - CE Predict/Explain A person flips a coin into the...Ch. 4 - CE Predict/Explain Suppose the elevator in the...Ch. 4 - A train moving with constant velocity travels 170...Ch. 4 - A tennis ball is struck in such a way that it...Ch. 4 - A person tosses a ball for her puppy to retrieve....Ch. 4 - An osprey flies horizontally with a constant speed...Ch. 4 - Predict/Calculate A hot-air balloon rises from the...Ch. 4 - In a friendly neighborhood squirt gun contest a...Ch. 4 - BIO Spitting Llamas An agitated llama may spit to...Ch. 4 - A particle leaves the origin with an initial...Ch. 4 - BIO When the dried-up seed pod of a scotch broom...Ch. 4 - Trick Shot In an Internet video an athlete...Ch. 4 - A shot-putter throws the shot with an initial...Ch. 4 - Two marbles are launched at t = 0 in the...Ch. 4 - Rescue Swimmers Coast Guard rescue swimmers are...Ch. 4 - A football player kicks a field goal, launching...Ch. 4 - A ball thrown straight upward returns to its...Ch. 4 - Predict/Calculate To decide who pays for lunch, a...Ch. 4 - Predict/Calculate A cannon is placed at the bottom...Ch. 4 - A golfer hits a shot to an elevated green. 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Most projectiles...Ch. 4 - Caterpillar Pellets The larvae (caterpillars) of...Ch. 4 - Caterpillar Pellets The larvae (caterpillars) of...Ch. 4 - Caterpillar Pellets The larvae (caterpillars) of...Ch. 4 - Caterpillar Pellets The larvae (caterpillars) of...Ch. 4 - Referring to Example 4-9 (a) At what launch angle...Ch. 4 - Referring to Example 4-9 Suppose that the golf...Ch. 4 - Referring to Example 4-11 Suppose the ball is...Ch. 4 - Predict/Calculate Referring to Example 4-11...
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