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Chapter 2: Problem 62

The wind is blowing from west to east at 35 \(\mathrm{mph}\) , and an eagle in that wind is flying at 22 mph relative to the air. What is the velocity of this eagle relative to a person standing on the ground if the eagle is flying (a) from west to east relative to the air and (b) from east to west relative to the air?

Short Answer

Expert verified
(a) 57 mph; (b) 13 mph.

Step by step solution

01

Understand the Problem

We need to find the eagle's velocity relative to a person on the ground in two different scenarios: when the eagle flies west to east and when it flies east to west, with the wind speed also playing a role in each case.
02

Calculating Velocity (a) West to East

When the eagle flies from west to east, its velocity relative to the air is 22 mph. Since the wind is also blowing from west to east at 35 mph, these velocities add up. The eagle's velocity relative to the ground is calculated as: \[ 22 ext{ mph} + 35 ext{ mph} = 57 ext{ mph} \]
03

Calculating Velocity (b) East to West

If the eagle is flying east to west, its velocity relative to the air is 22 mph, opposing the wind. We subtract the eagle's air speed from the wind speed to get the velocity relative to the ground: \[ 35 ext{ mph} - 22 ext{ mph} = 13 ext{ mph} \]. Since the eagle and the wind are in opposite directions, the ground speed is the difference.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Relative Velocity
Relative velocity is a key concept when determining how the movement of one object is perceived by another object. In this exercise, you need to consider both the velocity of the eagle and the velocity of the wind. The eagle's motion as seen by someone on the ground doesn't just depend on the eagle's flight speed. Relative velocity is basically the vector sum or difference of the primary velocities involved.
  • In the eagle's case, its velocity relative to the ground depends on its velocity relative to the air and the velocity of the wind.
  • If both movements are in the same direction, you add their speeds.
  • If they are in opposite directions, you subtract onespeed from the other.
Understanding how to calculate relative velocity is crucial in problems involving multiple moving references.
Wind Effect
The wind effect impacts how motion is perceived and can significantly alter traveling speeds. Winds can either aid or hinder, depending on their direction relative to the traveler. In this problem, the wind blows from west to east at a speed of 35 mph.
  • When the wind assists the flight of an eagle flying in the same direction, the speed increases.
  • When opposing, it reduces the effective speed.
Learning to factor in wind speed and its direction is essential, especially for activities like boating, flying, or even jogging on windy days. This is because the true speed over the ground can vary drastically based on the wind's impact.
Direction of Motion
Direction plays a vital role when calculating velocity relative to another observer. Simply knowing the speeds involved is not enough without the vector directions in which those speeds act. The direction is key to determining whether to add or subtract speeds.
  • When both the eagle's and wind's directions are from west to east, we add their speeds.
  • If the eagle flies east to west while the wind is west to east, their speeds oppose each other, and thus we subtract.
Understanding direction and its effect on motion is crucial. It helps us break down motion into coordinate systems or vectors to solve problems more efficiently.
Ground Speed Calculation
Ground speed is the actual speed at which an object travels over the surface of the Earth, and is vital for navigation. In this exercise, it is the eagle's speed as perceived by someone standing still on the ground. The calculation of ground speed involves assessing the combined effects of the bird's speed and the wind.
  • For example, if the eagle flies west to east at 22 mph and the wind aids it with 35 mph, their ground speed sums to 57 mph.
  • Conversely, if it flies east to west with the same relative speed against the 35 mph wind, the ground speed is 13 mph, determined by subtracting the eagle's speed from the opposing wind.
Calculating ground speed accurately is essential in air travel to ensure timely and efficient travel routes. All navigation relies on precise understanding of this concept.

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Most popular questions from this chapter

Prevention of hip fractures. Falls resulting in hip fractures are a major cause of injury and even death to the elderly. Typically, the hip's speed at impact is about 2.0 \(\mathrm{m} / \mathrm{s}\) . If this can be reduced to 1.3 \(\mathrm{m} / \mathrm{s}\) or less, the hip will usually not fracture. One way to do this is by wearing elastic hip pads. (a) If a typical pad is 5.0 \(\mathrm{cm}\) thick and compresses by 2.0 \(\mathrm{cm}\) during the impact of a fall, what acceleration (in \(\mathrm{m} / \mathrm{s}^{2}\) and in \(g^{\prime}\) s) does the hip undergo to reduce its speed to 1.3 \(\mathrm{m} / \mathrm{s} ?\) (b) The acceleration you found in part (a) may seem like a rather large acceleration, but to fully assess its effects on the hip, calculate how long it lasts.

\(\cdot\) If a pilot accelerates at more than 4\(g\) , he begins to "gray out," but not completely lose consciousness. (a) What is the shortest time that a jet pilot starting from rest can take to reach Mach 4 (four times the speed of sound) without graying out? (b) How far would the plane travel during this period of acceleration? (Use 331 \(\mathrm{m} / \mathrm{s}\) for the speed of sound in cold air.)

Two stones are thrown vertically upward from the ground, one with three times the initial speed of the other. (a) If the faster stone takes 10 s to return to the ground, how long will it take the slower stone to return? (b) If the slower stone reaches a maximum height of \(H,\) how high (in terms of \(H )\) will the faster stone go? Assume free fall.

Sound travels at a speed of about 344 \(\mathrm{m} / \mathrm{s}\) in air. You see a distant flash of lightning and hear the thunder arrive 7.5 seconds later. How many miles away was the lightning strike? (Assume the light takes essentially no time to reach you.)

Two runners start simultaneously at opposite ends of a 200.0 \(\mathrm{m}\) track and run toward each other. Runner \(A\) runs at a steady 8.0 \(\mathrm{m} / \mathrm{s}\) and runner \(B\) runs at a constant 7.0 \(\mathrm{m} / \mathrm{s} .\) When and where will these runners meet?
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