Answered: Serena Willliams hits a ball 2.25 m…

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

Serena Willliams hits a ball 2.25 m above the ground. The ball leaves her racquet with a speed of 16 m/s at an angle of 2° above the horizontal. The horizontal distance to the net is 7.0 m and the net is 1.0 m high. Assuming that the local acceleration due to gravity is 9.80 m/s², determine the distance (in m) between the ball and the top of the net at the moment the ball reaches the net (positive - the ball is above the net and negative - the ball is below the net).

Expert Solution

Step 1: Given data

Given

The initial height of the ball is $y subscript i equals 2.25 space straight m$ .
The initial speed of the ball is $u equals 16 space straight m divided by straight s$ .
The angle of projection is $theta equals 2 degree$ .
The range of the projectile (horizontal distance to the net) is R = 7 m.
The height of the net is h = 1 m.
The acceleration of gravity is g =9.80 m/s².

The horizontal component of velocity is,

$table row cell u subscript x end cell equals cell u cross times cos theta end cell row blank equals cell 16 space straight m divided by straight s cross times cos 2 degree end cell row blank equals cell 15.99 space straight m divided by straight s end cell end table$