Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Question: A hot-air balloon is ascending at the rate of $12 m / s$ and role="math" localid="1662959960903" $80 m$ is above the ground when a package is dropped over the side. (a) How long does the package take to reach the ground? (b) With what speed does it hit the ground?

Time (t) taken by the package to reach the ground is 5.45 sec.
Velocity (v) at which the package will hit the ground is 41.38 m/s.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

Initial speed for package, $(V_{\circ}) = - 12 m / s$

Height from which package is ${v_{f}}^{2} = v_{0}^{2} + 2as$ dropped $s = 80 m$

Acceleration=Gravitational Acceleration $a = 9.8 m / s^{2}$

Step 2: Understanding the concept

The problem deals with the kinematic equation of motion in which the motion of an object is described at constant acceleration. Using the Kinematic equation, the velocity and time to reach the ground dropped from hot air balloon at height $80 m$ can be calculated.

Step 3: First and second kinematic equation

The velocity in kinematic equation is expressed as,

(i) $v_{f} = v_{0} + at$

(ii) 41 m/s

Step 4: Determination of speed of package hits the ground

Consider downward as positive and upward as negative.

Calculate velocity (Part b), which can then be used in the calculation of time.

The balloon is ascending at the rate of -12m/s, and the package is dropped over the side.

Using equation (i), the final velocity will be

${v_{f}}^{2} = 1712 m^{2} {/s}^{2}$

$v_{f} = 41.38 m/s$

The velocity of the package when it hits the ground is 41.38 m/s

Step 5: Determination of time taken by package to hits the ground

Using equation (ii),

$v_{f} = v_{0} + at$

$41.38 m / s = - 12 m / s + 9.8 m / s^{2} \times t 53.38 m / s = 9.8 m / s^{2} \times t t = \frac{53.38 m / s}{9.8 m / s^{2}} = 5.4469 \sec \approx 5.45 \sec$

The time taken by the packet to reach the ground is 5.45sec.

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Fundamentals Of Physics

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Short Answer

Question: A hot-air balloon is ascending at the rate of $12 m / s$ and role="math" localid="1662959960903" $80 m$ is above the ground when a package is dropped over the side. (a) How long does the package take to reach the ground? (b) With what speed does it hit the ground?

Step by Step Solution

Step 1: Given information

Step 2: Understanding the concept

Step 3: First and second kinematic equation

Step 4: Determination of speed of package hits the ground

Step 5: Determination of time taken by package to hits the ground

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Fundamentals Of Physics

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Short Answer

Question: A hot-air balloon is ascending at the rate of 12 m/s and role="math" localid="1662959960903" 80mis above the ground when a package is dropped over the side. (a) How long does the package take to reach the ground? (b) With what speed does it hit the ground?

Step by Step Solution

Step 1: Given information

Step 2: Understanding the concept

Step 3: First and second kinematic equation

Step 4: Determination of speed of package hits the ground

Step 5: Determination of time taken by package to hits the ground

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Question: A hot-air balloon is ascending at the rate of $12 m / s$ and role="math" localid="1662959960903" $80 m$ is above the ground when a package is dropped over the side. (a) How long does the package take to reach the ground? (b) With what speed does it hit the ground?