Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

Answers without the blur.

Just sign up for free and you're in.

Short Answer

In a forward punch in karate, the fist begins at rest at the waist and is brought rapidly forward until the arm is fully extended. The speed $v (t)$ of the fist is given in figure for someone skilled in karate. The vertical scaling is set by $v_{s} = 8.0 m / s .$ . How far has the first moved at (a) time $t = 50 ms$ (b) when the speed of the fist is maximum?

(a) Position of a fist at a certain time is 0.13 meters

(b) Distance when the speed of fist is maximum 0.50 meters

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

The graph of v (m/s) vs t (s) with the vertical scale set by $v_{s} = 8.0 m / s .$ .

Step 2: Area under the curve

The calculation of the region bounded by the curve within the given graph is called the area under the curve. The area under the curve will give the distance covered by the fist.

Step 3: (a) Calculations to find out the position of an object at any time to find the area under the curve:

We need to divide that area into two parts, to compute the position of the object at $t_{1} = 50 ms$ ,

The first part is from.0 to 10 ms The area has the shape of a triangle so the area under the curve is,

$Area of triangle (A) = 0.01 meters$

2^nd part is from 10 to 50 ms that area has the shape of a trapezoid, so the area under the curve is,

$Area of trapezoid (B) = \frac{1}{2} \times 0.040 \sec \times (2 + 4) m / s = 0.12 m$

Now, $Area of triangle + Area of trapezoid = 0.13 m$

Hence, the fist is at 0.13 m distance at 0.050 sec

Step 4: (b) Calculations for distance at which fist has maximum velocity:

From the graph, we conclude the following statement

The maximum speed is at $t = 0.120 \sec .$

We need to find the area under the curve for regions between 0.050 sec to 0.090 sec and 0.090 sec to 0.120 sec.

Now, the area under the curve between 0.050 to 0.090 sec. is shaped as a trapezoid is,

$Area of trapezoid (C) = \frac{1}{2} \times (0.040 \sec) \times (4 + 5 m / s) = 0.18 m$

The area under the curve between 0.090 to 0.120 sec is shaped as a trapezoid,

role="math" localid="1656158740938" $Area of trapezoid (D) = \frac{1}{2} \times (0.030 \sec) \times (5 + 7.5 m / s) = 0.19 m$

Therefore, the total area under the curve is $(A_{T})$ ,

$A_{T} = A + B + C + D = 0.01 + 0.12 + 0.18 + 0.19 = 0.50 m$

So, the distance covered by the fist at maximum speed is 0.50 m .

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Given data

Step 2: Area under the curve

Step 3: (a) Calculations to find out the position of an object at any time to find the area under the curve:

Step 4: (b) Calculations for distance at which fist has maximum velocity:

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Given data

Step 2: Area under the curve

Step 3: (a) Calculations to find out the position of an object at any time to find the area under the curve:

Step 4: (b) Calculations for distance at which fist has maximum velocity:

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Famous Physicists

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics