Answered: position vector in unit-vector notation…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

The acceleration of a particle moving only on a horizontal xy plane is given by ?→=5??ˆ+6??ˆa→=5ti^+6tj^, where ?→a→ is in meters per second-squared and t is in seconds. At t = 0, the position vector ?→=(26.0m)?ˆ+(36.0m)?ˆr→=(26.0m)i^+(36.0m)j^ locates the paticle, which then has the velocity vector ?→=(6.70m/s)?ˆ+(1.90m/s)?ˆv→=(6.70m/s)i^+(1.90m/s)j^. At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b)the angle between its direction of travel and the positive direction of the x axis?

Expert Solution

Step 1

Given:

Particle is moving in xy-plane.

Acceleration vector is $\vec{a} = (5 t) \hat{i} + (6 t) \hat{j}$ ; here acceleration is in units of $m / s^{2}$ and $t$ is time in seconds.

At time $t = 0 s$ , position vector is $\vec{r} (0 s) = (26 m) \hat{i} + (36 m) \hat{j}$

and its velocity vector is $\vec{v} (0 s) = (6.70 m / s) \hat{i} + (1.90 m / s) \hat{j}$

Find:

(a) At time $t = 4.60 s$ , write position vector in unit-vector notation.

(b) Angle between direction of travel and positive direction of x-axis.

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