Explanation Given: r = ( A t cos t ) i + ( A t 2 + 1 ) j + ( B t sin t ) k r = ( A t cos t ) i + ( A t 2 + 1 ) j + ( B t sin t ) k Or: x = A t cos t y = A t 2 + 1 z = B t sin t Then cos t = x A t sin t = z B t t 2 = ( y A ) 2 − 1 Now cos 2 t + sin 2 t = 1 ⇒ ( x A t ) 2 + ( z B t ) 2 = 1 Or: t 2 = ( x A ) 2 + ( z B ) 2 Then ( y A ) 2 − 1 = ( x A ) 2 + ( z B ) 2 Or: ( y A ) 2 − ( x A ) 2 − ( z B ) 2 = 1 ( Q . E To determine (b) Smallest nonzero value of t for which the position vector and the velocity are perpendicular to each other.

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 11.4, Problem 11.96P

To determine

(a)

Magnitude of velocity and acceleration when t=0.

To determine

(b)

Smallest nonzero value of t for which the position vector and the velocity are perpendicular to each other.

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Chapter 11.4, Problem 11.95P

Chapter 11.4, Problem 11.97P

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Vector Mechanics for Engineers: Dynamics

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(a) Magnitude of velocity and acceleration when t = 0 .

Solution Summary: The author explains the magnitude of velocity and acceleration when t=0.

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(a)

Magnitude of velocity and acceleration when t=0.

(b)

Smallest nonzero value of t for which the position vector and the velocity are perpendicular to each other.

Want to see the full answer?

Chapter 11 Solutions

(a) Magnitude of velocity and acceleration when t = 0 .

Solution Summary: The author explains the magnitude of velocity and acceleration when t=0.

Concept explainers

Videos

(a) Magnitude of velocity and acceleration when t=0.

(b) Smallest nonzero value of t for which the position vector and the velocity are perpendicular to each other.

Want to see the full answer?

Chapter 11 Solutions

(a)

Magnitude of velocity and acceleration when t=0.

(b)

Smallest nonzero value of t for which the position vector and the velocity are perpendicular to each other.