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19. A particle starts at the origin with initial velocity

19. A particle starts at the origin with initial velocity

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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It 0 r(3), r(3.2) X 17. A particle moves with position function r(t) = t ln ti+tj+ek. Find the velocity, speed, and acceleration of the particle. 18. Find the velocity, speed, and acceleration of a particle mov- ing with position function r(t) = (2t² − 3) i + 2tj. Sketch the path of the particle and draw the position, velocity, and acceleration vectors for t = 1. 19. A particle starts at the origin with initial velocity i- j + 3k. Its acceleration is a(t) = 6ti + 12t² j - 6tk. Find its position function. 20. An athlete throws a shot at an angle of 45° to the horizontal at an initial speed of 43 ft/s. It leaves his hand 7 ft above the ground. URT (a) Where is the shot 2 seconds later? (b) How high does the shot go? (c) Where does the shot land? 21. A projectile is launched with an initial speed of 40 m/s from the floor of a tunnel whose height is 30 m. What angle of elevation should be used to achieve the maximum possible horizontal range of the projectile? What is the maximum range? 22. Find the tangential and normal components of the accelera- tion vector of a particle with position function
Transcribed Image Text:It 0 r(3), r(3.2) X 17. A particle moves with position function r(t) = t ln ti+tj+ek. Find the velocity, speed, and acceleration of the particle. 18. Find the velocity, speed, and acceleration of a particle mov- ing with position function r(t) = (2t² − 3) i + 2tj. Sketch the path of the particle and draw the position, velocity, and acceleration vectors for t = 1. 19. A particle starts at the origin with initial velocity i- j + 3k. Its acceleration is a(t) = 6ti + 12t² j - 6tk. Find its position function. 20. An athlete throws a shot at an angle of 45° to the horizontal at an initial speed of 43 ft/s. It leaves his hand 7 ft above the ground. URT (a) Where is the shot 2 seconds later? (b) How high does the shot go? (c) Where does the shot land? 21. A projectile is launched with an initial speed of 40 m/s from the floor of a tunnel whose height is 30 m. What angle of elevation should be used to achieve the maximum possible horizontal range of the projectile? What is the maximum range? 22. Find the tangential and normal components of the accelera- tion vector of a particle with position function
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