Explanation Given info: The cannon fires a projectile to the right with a speed of v 0 relative to the train from a barrel elevated at an angle θ , the speed of the train is v train and the acceleration of the train is a . The following figure shows the initial and final position of the motion of the projectile with respect to the cannon. Figure I Formula to calculate the period of flight of the projectile is, t = 2 v 0 sin θ g t is the period of the flight. v 0 is the initial velocity of the projectile. θ is the launch angle. g is the acceleration due to gravity. Formula to calculate the horizontal distance traveled by the projectile is, ( x 1 ) p = ( v 0 cos θ + v train ) t ( x 1 ) p is the horizontal distance traveled by the projectile. v train is the speed of the train. Substitute 2 v o sin θ g for t in the above equation to find ( x 1 ) p . ( x 1 ) p = ( v 0 cos θ + v train ) ( 2 v o sin θ g ) = 2 v 0 2 sin θ cos θ g + 2 v 0 v train sin θ g Formula to calculate the horizontal distance traveled by train is, ( x 1 ) T = v train t + 1 2 a t 2 ( x 1 ) T is the horizontal distance traveled by train. a is the acceleration of the train. Substitute 2 v o sin θ g for t in the above equation to find ( x 1 ) T . ( x 1 ) T = v train ( 2 v o sin θ g ) + 1 2 a ( 2 v o sin θ g ) 2 = 2 v 0 v train sin θ g + 2 a v 0 2 sin 2 θ g 2 Formula to calculate the range of the projectile from the shown figure (I) is R = ( x 1 ) p − ( x 1 ) T R is the range of the projectile. ( x 1 ) p is the final position of the projectile. ( x 1 ) T is the final position of the train

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

4th Edition

ISBN: 9780133942651

Author: Randall D. Knight (Professor Emeritus)

Publisher: PEARSON

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Chapter 4, Problem 84EAP

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The expression for the angle at which the projectile must be fired so that it lands as far as possible from the cannon.

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Chapter 4, Problem 83EAP

Chapter 4, Problem 85EAP

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Chapter 4 Solutions

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Ch. 4 - a. At this instant, is the particle in FIGURE Q4.1...Ch. 4 - a. At this instant, is the particle in FIGURE Q4.2...Ch. 4 - Tarzan swings through the jungle by hanging from a...Ch. 4 - A projectile is launched at an angle of 30°. a. Is...Ch. 4 - For a projectile, which of the following...Ch. 4 - A cart that is rolling at constant velocity on a...Ch. 4 - A rock is thrown from a bridge at an angle 30°...Ch. 4 - Anita is running to the right at 5 m/s in FIGURE...Ch. 4 - An electromagnet on the ceiling of an airplane...Ch. 4 - Zack is driving past his house in FIGURE Q4.1O. He...

Ch. 4 - II. In FIGURE Q4.11. Yvette and Zack are driving...Ch. 4 - In uniform circular motion, which of the following...Ch. 4 - FIGURE Q4.13 shows three points on a steadily...Ch. 4 - FIGURE Q4.14 shows four rotating wheels. For each,...Ch. 4 - FIGURE Q4.15 shows a pendulum at one end point of...Ch. 4 - Problems I and 2 show a partial motion diagram....Ch. 4 - Prob. 2EAP Ch. 4 - Answer Problems 3 through 5 by choosing one of the...Ch. 4 - Answer Problems 3 through 5 by choosing one of the...Ch. 4 - Answer Problems 3 through 5 by choosing one of the...Ch. 4 - A rocket-powered hockey puck moves on a horizontal...Ch. 4 - A rocket-powered hockey puck moves on a horizontal...Ch. 4 - Prob. 8EAP Ch. 4 - A particle moving in the xy- plane has velocity v...Ch. 4 - You have a remote-controlled car that has been...Ch. 4 - A ball thrown horizontally at 25 m/s travels a...Ch. 4 - A physics student on the Planet Exidor throws a...Ch. 4 - A supply plane needs to drop a package of food to...Ch. 4 - A rifle is aimed horizontally at a target 50 m...Ch. 4 - In the Olympic shotput event, an athlete throws...Ch. 4 - On the Apollo 14 mission to the moon, astronaut...Ch. 4 - A baseball player friend of yours wants to...Ch. 4 - A boat takes 3.0 hours to travel 30 km down a...Ch. 4 - When the moving sidewalk at the airport is broken,...Ch. 4 - Prob. 20EAP Ch. 4 - A kayaker, needs to paddle north across a...Ch. 4 - Susan, driving north at 60 mph, and Trent, driving...Ch. 4 - FIGURE EX4.23 shows the...Ch. 4 - FIGURE EX4.24 shows the...Ch. 4 - FIGURE EX4.25 shows the...Ch. 4 - The earth’s radius is about 4000 miles. Kampala,...Ch. 4 - An old-fashioned single-play vinyl record rotates...Ch. 4 - As the earth mates, what is the speed of (a) a...Ch. 4 - How fast must a plane fly along the earth’s...Ch. 4 - A 3000-rn-high mountain is located on the equator....Ch. 4 - Peregrine falcons are known for their maneuvering...Ch. 4 - To withstand “g-forces” of up to 10 g’s, caused by...Ch. 4 - The radius of the earth’s very nearly circular...Ch. 4 - A speck of dust on a spinning DVD has a...Ch. 4 - Your roommate is working on his bicycle and has...Ch. 4 - I FIGURE EX4.36 shows the angular velocity graph...Ch. 4 - I FIGURE EX4.37 shows the angular acceleration...Ch. 4 - FIGURE EX4.38 shows the...Ch. 4 - A wheel initially rotating at 60 rpm experiences...Ch. 4 - A 5.0-rn-diameter merry-go-round is initially...Ch. 4 - An electric fan goes from rest to 1800 rpm in 4.0...Ch. 4 - A bicycle wheel is rotating at 50 rpm when the...Ch. 4 - Starting from rest, a DVD steadily accelerates to...Ch. 4 - A spaceship maneuvering near Planet Zeta is...Ch. 4 - equation reference goes here45. A particle moving...Ch. 4 - A projectile’s horizontal range over level ground...Ch. 4 - a. A projectile is launched with speed v0and angle...Ch. 4 - A projectile is launched from ground level at...Ch. 4 - A gray kangaroo can bound across level ground with...Ch. 4 - A ball is thrown toward a cliff of height h with a...Ch. 4 - A tennis player hits a ball 2.0 m above the...Ch. 4 - You are target shooting using a toy gun that fires...Ch. 4 - A 35 g steel ball is held by a ceiling-mounted...Ch. 4 - You are watching an archery tournament when you...Ch. 4 - You’re 6.0 m from one wall of the house seen in...Ch. 4 - Sand moves without slipping at 6.0 m/s down a...Ch. 4 - A stunt man drives a car at a speed of 20 m/s off...Ch. 4 - A javelin thrower standing at rest holds the...Ch. 4 - A rubber ball is dropped onto a ramp that is...Ch. 4 - You are asked to consult for the city’s research...Ch. 4 - Ships A and B leave port together. For the next...Ch. 4 - While driving north at 25 m/s during a rainstorm...Ch. 4 - You’ve been assigned the task of using a shaft...Ch. 4 - Prob. 64EAP Ch. 4 - Prob. 65EAP Ch. 4 - Astronauts use a centrifuge to simulate the...Ch. 4 - Communications satellites are placed in a circular...Ch. 4 - Prob. 68EAP Ch. 4 - A high-speed drill rotating ccw at 2400 rpm comes...Ch. 4 - A turbine is spinning at 3800 rpm. Frication in...Ch. 4 - Prob. 71EAP Ch. 4 - The angular velocity of a process control motor is...Ch. 4 - A Ferris wheel of radius R speeds up with angular...Ch. 4 - Prob. 74EAP Ch. 4 - A painted tooth on a spinning gear has angular...Ch. 4 - A car starts from rest on a curve with radius of...Ch. 4 - Prob. 77EAP Ch. 4 - In Problem 78 through 80 you are given the...Ch. 4 - Prob. 79EAP Ch. 4 - In Problem 78 through 80 you are given the...Ch. 4 - In one contest at the country fair, seen in FIGURE...Ch. 4 - Prob. 82EAP Ch. 4 - Prob. 83EAP Ch. 4 - Prob. 84EAP Ch. 4 - Prob. 85EAP

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