Answered: A baseball reaches Peter with a…

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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A baseball reaches Peter with a velocity of 41.6 m/s at -5.00 degrees from the horizontal.

Peter strikes the ball and it leaves the bat with a velocity of 45.1 m/s at 153 degrees. What is the ball's change in velocity?

Expert Solution

Step 1

In vector components we can write

$\begin{array}{rcl} {\vec{v}}_{i n i t i a l} & = & v_{i n i t i a l} \cos (- 5 °) \vec{i} + v_{i n i t i a l} \sin (- 5 °) \vec{j} \\ = & 41.6 \cos (- 5 °) \vec{i} + 41.6 \sin (- 5 °) \vec{j} \\ = & 41.442 \vec{i} - 3.626 \vec{j} \end{array}$

and for final velocity,

$\begin{array}{rcl} {\vec{v}}_{f i n a l} & = & v_{f i n a l} \cos (153 °) \vec{i} + v_{f i n a l} \sin (153 °) \vec{j} \\ = & 45.1 \cos (153 °) \vec{i} + 45.1 \sin (153 °) \vec{j} \\ = & - 40.184 \vec{i} + 20.475 \vec{j} \end{array}$

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