Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

An eagle is flying horizontally at a speed of $3.00$ m/s when the fish in her talons wiggles loose and falls into the lake $5.00$ m below. Calculate the velocity of the fish relative to the water when it hits the water.

The final velocity of the fish relative to water when it hits the water, v_f = $10.3$ m/s.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Definition of final velocity

When gravity first exerts a force on an item, its initial velocity indicates how fast it travels. The final velocity, on the other hand, is a vector number that measures a moving body's speed and direction after it has reached its maximum acceleration.

Given data:

Speed of the eagle in the x-direction, v_ix = $3.00$ m/s.
Vertical displacement of the fish to the lake, ∆y = $5.00$ m.
The initial vertical component, v_iy = 0 m/s.
Acceleration of the fish in the vertical direction, a_y = - $- 9.8$ m/s².

Step 2: Finding final velocity of fish

To find the final velocity in the negative y-direction, we have the kinematic equation

${V_{f y}}^{2} = {V_{i}}^{2} + 2 a_{y} ∆ Y$

Substitute the values in the above equation, we get

${V_{f y}}^{2} = 0 + 2 \times (- 9.8) \times (- 5.00) {V_{f y}}^{2} = 98 V_{f y} = \pm \sqrt{98} = \pm 9.9 m / s$

We take only the negative value because of this velocity in the negative y-direction.

So, $V_{f y} = - 9.9 m / s$

Now acceleration in the horizontal direction, a_x= 0 m/s²{since, g = 0 m/s²}.

So the final velocity of the fish in the x-direction is equal to the initial velocity of the fish in the x-direction $3.00$ = m/s.

That is, $V_{f x} = V_{i x} = 3.00 m / s$

So we have, $V_{f x} = 3.00 m / s$ and $V_{f y} = - 9.90 m / s$

These two velocities are the two components of the final velocity of the fish, v_f .

The resultant vector

$V_{f} = \sqrt{{(3.00)}^{2} + {(- 9.90)}^{2}} = 10.3 m / s$

The final velocity of the fish is 10.3 m/s.

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College Physics (Urone)

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Short Answer

An eagle is flying horizontally at a speed of $3.00$ m/s when the fish in her talons wiggles loose and falls into the lake $5.00$ m below. Calculate the velocity of the fish relative to the water when it hits the water.

Step by Step Solution

Step 1: Definition of final velocity

Step 2: Finding final velocity of fish

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College Physics (Urone)

Answers without the blur.

Short Answer

An eagle is flying horizontally at a speed of 3.00m/s when the fish in her talons wiggles loose and falls into the lake 5.00 m below. Calculate the velocity of the fish relative to the water when it hits the water.

Step by Step Solution

Step 1: Definition of final velocity

Step 2: Finding final velocity of fish

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An eagle is flying horizontally at a speed of $3.00$ m/s when the fish in her talons wiggles loose and falls into the lake $5.00$ m below. Calculate the velocity of the fish relative to the water when it hits the water.