Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

Suppose a soccer player kicks the ball from a distance 30 m toward the goal. Find the initial speed of the ball if it just passes over the goal, 2.4 m above the ground, given the initial direction to be 40º above the horizontal.

The initial velocity of the ball will be 18.1 m/s.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

The change in the displacement in the y-direction is 2.4 meters.
The acceleration in the above case is -9.8 m/s².

Step 2: Initial velocity of the ball

Figure: The motion of the ball

The initial velocity in the x-direction can be caculated as:

$\begin{array}{rcl} c o s θ & = & \frac{a}{h} \\ \cos 40 & = & \frac{V_{i x}}{V_{i}} \\ V_{i x} & = & V_{i} \cos 40^{°} \end{array}$

The initial velocity in the x-direction is the above equation.

The initial velocity in the y-direction can be caculated as:

$\begin{array}{rcl} s i n θ & = & \frac{o}{h} \\ \sin 40 & = & \frac{V_{i y}}{V_{i}} \\ V_{i y} & = & V_{i} \sin 40 \end{array}$

The initial velocity in the y-direction is above the equation.

The velocity in the x frame will be constant at all times. Considering the initial velocity, we can write:

$\begin{array}{rcl} V & = & \frac{x}{t} \\ V_{i x} & = & \frac{30}{t} \\ t & = & \frac{30}{V_{i} \cos 40} \end{array}$

The time taken is used from the above equation.

From the equation of motion:

$∆ Y = V_{i y} t + \frac{1}{2} a_{y} t^{2}$

By putting the values in the above equation, we get:

$\begin{array}{rcl} 2.4 & = & (V_{i} \sin 40) (\frac{30}{V_{i} \cos 40}) + \frac{1}{2} (- 9.8) {(\frac{30}{V_{i} \cos 40})}^{2} \\ 2.4 & = & 25.2 - \frac{4410}{{V_{i}}^{2} \times 0.587} \\ \frac{4410}{{V_{i}}^{2} \times 0.587} & = & 25.2 - 2.4 \\ {V_{i}}^{2} & = & \frac{7510}{22.8} \\ {V_{i}}^{2} & = & 329 \\ V_{i} & = & 18.1 \frac{m}{s} \end{array}$

Therefore, the initial velocity will be 18.1 m/s.

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College Physics (Urone)

Answers without the blur.

Short Answer

Suppose a soccer player kicks the ball from a distance 30 m toward the goal. Find the initial speed of the ball if it just passes over the goal, 2.4 m above the ground, given the initial direction to be 40º above the horizontal.

Step by Step Solution

Step 1: Given data

Step 2: Initial velocity of the ball

Most popular questions for Physics Textbooks

A ball is kicked with an initial velocity of \(16\,m/s\) in the horizontal direction and \(12\,m/s\) in the vertical direction. (a) At what speed does the ball hit the ground? (b) For how long does the ball remain in the air? (c) What maximum height is attained by the ball?

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Select your language

College Physics (Urone)

Answers without the blur.

Short Answer

Suppose a soccer player kicks the ball from a distance 30 m toward the goal. Find the initial speed of the ball if it just passes over the goal, 2.4 m above the ground, given the initial direction to be 40º above the horizontal.

Step by Step Solution

Step 1: Given data

Step 2: Initial velocity of the ball

Most popular questions for Physics Textbooks

A ball is kicked with an initial velocity of \(16\,m/s\) in the horizontal direction and \(12\,m/s\) in the vertical direction. (a) At what speed does the ball hit the ground? (b) For how long does the ball remain in the air? (c) What maximum height is attained by the ball?

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