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Challenge Problem 2 The time-dependent displacement vector of a particle is defined as * = (6.00t³ - 1.90t² - 6.00t)î - (4.10t + 1.32t² — 19)ĵ+√1.08t³ + 14.0t k - where all components are in meters. (a) What is the angle between the instantaneous position and instantaneous velocity v at the instant that ry = 0 m? (b) What is the angle between the instantaneous position and instantaneous acceleration a at the instant that vx is maximum? (c) Find the unit vector that points perpendicular to both the instantaneous position and instantaneous velocity at the instant that t = 4.00 s, and that has a positive z-component.

Challenge Problem 2 The time-dependent displacement vector of a particle is defined as * = (6.00t³ - 1.90t² - 6.00t)î - (4.10t + 1.32t² — 19)ĵ+√1.08t³ + 14.0t k - where all components are in meters. (a) What is the angle between the instantaneous position and instantaneous velocity v at the instant that ry = 0 m? (b) What is the angle between the instantaneous position and instantaneous acceleration a at the instant that vx is maximum? (c) Find the unit vector that points perpendicular to both the instantaneous position and instantaneous velocity at the instant that t = 4.00 s, and that has a positive z-component.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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Challenge Problem 2 The time-dependent displacement vector of a particle is defined as r = (6.00t³ — 1.90t² – 6.00t)î — (4.10t + 1.32t² – 19)ĵ + √1.08t³ + 14.0t k where all components are in meters. (a) What is the angle between the instantaneous position ở and instantaneous velocity v at the instant that ry = 0 m? (b) What is the angle between the instantaneous position and instantaneous acceleration à at the instant that v is maximum? (c) Find the unit vector that points perpendicular to both the instantaneous position and instantaneous velocity v at the instant that t = 4.00 s, and that has a positive z-component. (d) Find the unit vector that points perpendicular to both the instantaneous value of and instantaneous velocity à at the instant that vx = 0, and that has a positive y-component.
Transcribed Image Text:Challenge Problem 2 The time-dependent displacement vector of a particle is defined as r = (6.00t³ — 1.90t² – 6.00t)î — (4.10t + 1.32t² – 19)ĵ + √1.08t³ + 14.0t k where all components are in meters. (a) What is the angle between the instantaneous position ở and instantaneous velocity v at the instant that ry = 0 m? (b) What is the angle between the instantaneous position and instantaneous acceleration à at the instant that v is maximum? (c) Find the unit vector that points perpendicular to both the instantaneous position and instantaneous velocity v at the instant that t = 4.00 s, and that has a positive z-component. (d) Find the unit vector that points perpendicular to both the instantaneous value of and instantaneous velocity à at the instant that vx = 0, and that has a positive y-component.
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