To determine (a) The equation of rocket’s trajectory (b) Shape of trajectory (c) Elevation of rocket Explanation Part (a): Velocity is basically a speed of a particle in a particular direction with magnitude. It is the ratio of the displacement per unit time. It is expressed by the expression as given below: v = x t …… (1) Here, x is displacement traveled by the body in time t . The SI unit of velocity is meter per second m/s . So, the motion of rocket in horizontal x-direction is given by using equation (1) below: x = v x t v x = v cos θ = a x t …… (2) Here, θ is the angle formed with horizontal component. By using Newton’s equation of motion, the motion of rocket in vertical y-direction is given below: s = v t + 1 2 a t 2 y = v sin θ t − 1 2 a t 2 …… (3) Part (c): Total force F y in the y-direction is force of thrust in upward so F = F thrust sin θ and normal force in downward direction so F N = m g F y = m a y a y = F y m a y = F sin θ − m g m …… (4) Here, u is the initial velocity of the rocket, v is the final velocity of the rocket, and s is the distance covered the rocket. Initial velocity of the rocket in both the x- and y-direction is zero. So the expression for final velocity of the rocket to reach the speed of the sound is given as follows: v y 2 = 2 a y y y = v y 2 2 a y ……. (5) Given: Mass of interceptor rocket m = 5000 kg Thrust of rocket F thrust = 140700 N Speed of sound v = 330 m/s Rocket launched at angle θ = 44.7 ο Formula used: v = x t y = v sin θ t − 1 2 a t 2 F = m a Calculation: Part (a): Substitute, equation (2) in equation (3), so the equation in terms of y as a function of x that shows the rocket’s trajectory is given as follows: y ( x ) = v sin θ ( x v cos θ ) − 1 2 g ( x v x ) 2 y ( x ) = x tan θ − 1 2 g ( x v x ) 2 …… (6) Part (b): Equation (6) shows the equation of parabola and its axis is parallel to y-axis

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Chs 1-42) Plus Mastering Physics with Pearson eText -- Access Card Package (4th Edition)

4th Edition

ISBN: 9780133953145

Author: Randall D. Knight (Professor Emeritus)

Publisher: PEARSON

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Chapter 8, Problem 34EAP

To determine

(a) The equation of rocket’s trajectory

(b) Shape of trajectory

(c) Elevation of rocket

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Chapter 8, Problem 33EAP

Chapter 8, Problem 35EAP

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Chapter 8 Solutions

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Chs 1-42) Plus Mastering Physics with Pearson eText -- Access Card Package (4th Edition)

Ch. 8 - In uniform circular motion, which of the following...Ch. 8 - A car runs out of gas while driving down a hill....Ch. 8 - FIGURE Q8.3 is a bird's-eye view of particles on...Ch. 8 - Tarzan swings through the jungle on a massless...Ch. 8 - FIGURE Q8.5 shows two balls of equal mass moving...Ch. 8 - Ramon and Sally are observing a toy car speed up...Ch. 8 - A jet plane is flying on a level course at...Ch. 8 - A small projectile is launched parallel to the...Ch. 8 - 9. You can swing a ball on a string in a vertical...Ch. 8 - A golfer starts with the club over her head and...

Ch. 8 - As a science fair project, you want to launch an...Ch. 8 - A 500 g model rocket is on a cart that is rolling...Ch. 8 - A 4.0 × 1010 kg asteroid is heading directly...Ch. 8 - A 55 kg astronaut who weighs 180 N on a distant...Ch. 8 - A 1500 kg car drives around a flat 200-m-diameter...Ch. 8 - A 1500 kg car takes a 50-m-radius unbanked curve...Ch. 8 - A 200 g block on a 50-cm-long string swings in a...Ch. 8 - In the Bohr model of the hydrogen atom, an...Ch. 8 - Suppose the moon were held in its orbit not by...Ch. 8 - 10. A highway curve of radius 500 m is designed...Ch. 8 - It is proposed that future space stations create...Ch. 8 - A 5.0 g coin is placed 15 cm from the center of a...Ch. 8 - Mass m1on the frictionless table of FIGURE EX8.13...Ch. 8 - A satellite orbiting the moon very near the...Ch. 8 - What is free-fall acceleration toward the sun at...Ch. 8 - 16. A 9.4 × 1021 kg moon orbits a distant planet...Ch. 8 - Communications satellites are placed in circular...Ch. 8 - A car drives over the top of a hill that has a...Ch. 8 - The weight of passengers on a roller coaster...Ch. 8 - A roller coaster car crosses the top of a circular...Ch. 8 - The normal force equals the magnitude of the...Ch. 8 - A student has 65-cm-long arms. What is the minimum...Ch. 8 - While at the county fair, you decide to ride the...Ch. 8 - A 500 g ball swings in a vertical circle at the...Ch. 8 - A 500 g ball moves in a vertical circle on a...Ch. 8 - A heavy ball with a weight of 100 N (m = 10.2 kg)...Ch. 8 - A toy train rolls around a horizontal...Ch. 8 - 28. A new car is tested on a 200-m-diameter track....Ch. 8 - An 85,000 kg stunt plane performs a loop-the-loop,...Ch. 8 - Three cars are driving at 25 m/s along the road...Ch. 8 - Derive Equations 8.3 for the acceleration of a...Ch. 8 - 32. A 100 g bead slides along a frictionless wire...Ch. 8 - 33. Space scientists have a large test chamber...Ch. 8 - 34. A 5000 kg interceptor rocket is launched at an...Ch. 8 - Prob. 35EAP Ch. 8 - 36. A rocket- powered hockey puck has a thrust of...Ch. 8 - Prob. 37EAP Ch. 8 - A 2.0 kg projectile with initial velocity m/s...Ch. 8 - A 75 kg man weighs himself at the north pole and...Ch. 8 - A concrete highway curve of radius 70 m banked at...Ch. 8 - a. an object of mass m swings in horizontal circle...Ch. 8 - 42. You’ve taken your neighbor’s young child to...Ch. 8 - A 4.4-cm-diameter, 24 g plastic ball is attached...Ch. 8 - A charged particle of mass m moving with speed v...Ch. 8 - Two wires are tied to the 2.0 kg sphere shown in...Ch. 8 - Two wires are tied to the 300 g sphere shown in...Ch. 8 - A conical pendulum is formed by attaching a ball...Ch. 8 - The 10 mg bead in FIGURE P8.48 is free to slide on...Ch. 8 - In an old-fashioned amusement park ride,...Ch. 8 - The ultracentrifuge is an important tool for...Ch. 8 - In an amusement park ride called The Roundup,...Ch. 8 - 52. Suppose you swing a ball of mass m in a...Ch. 8 - A 30 g ball rolls around a 40-cm-diameter L-shaped...Ch. 8 - FIGURE P8.54 shows a small block of mass m sliding...Ch. 8 - The physics of circular motion sets an upper limit...Ch. 8 - A 100 g ball on a 60-cm-long string is swung in a...Ch. 8 - A 60 g ball is tied to the end of a 50-cm-long...Ch. 8 - Elm Street has a pronounced dip at the bottom of a...Ch. 8 - 59. A 100 g ball on a 60-cm-long string is swung...Ch. 8 - Scientists design a new particle accelerator in...Ch. 8 - 61. A 1500 kg car starts from rest and drives...Ch. 8 - Prob. 62EAP Ch. 8 - 63. A 2.0 kg ball swings in a vertical circle on...Ch. 8 - In Problems 64 and 65 you are given the equation...Ch. 8 - In Problems 64 and 65 you are given the equation...Ch. 8 - Sam (75 kg) takes off up a 50-m-high, 10°...Ch. 8 - In the absence of air resistance, a projectile...Ch. 8 - The father of Example 8.2 stands at the summit of...Ch. 8 - A small bead slides around a horizontal circle at...Ch. 8 - A 500 g steel block rotates on a steel table while...Ch. 8 - If a vertical cylinder of water (or any other...

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