3. A particle moves along a path such that its radius vector is given by f(t) = a sin(kt) ê, + b cos(kt) ê, where a, b, and k are constants. Show that the path is an ellipse of axes 2a and 2b. Show also, by expressing the acceleration in terms of the vector 7, that the acceleration is directed toward the origin at all times

3. A particle moves along a path such that its radius vector is given by f(t) = a sin(kt) ê, + b cos(kt) ê, where a, b, and k are constants. Show that the path is an ellipse of axes 2a and 2b. Show also, by expressing the acceleration in terms of the vector 7, that the acceleration is directed toward the origin at all times

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Motion In Two Dimensions

Section3.3: Projectile Motion

Problem 3.2QQ: (i) As a projectile thrown upward moves in its parabolic path (such as in Fig. 3.8), at what point...

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(i) As a projectile thrown upward moves in its parabolic path (such as in Fig. 3.8), at what point along its path are the velocity and acceleration vectors for the projectile perpendicular to each other? (a) nowhere (b) the highest point (c) the launch point (ii) From the same choices, at what point are the velocity and acceleration vectors for the projectile parallel to each other?
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