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Chapter 3: Q53PE (page 87)

A seagull flies at a velocity of 9.0 m/s straight into the wind.

(a) If it takes the bird 20 min to travel 6.0 km relative to the Earth, what is the velocity of the wind?

(b) If the bird turns around and flies with the wind, how long will he take to return 6.0 km?

(c) Discuss how the wind affects the total round-trip time compared to what it would be with no wind.

Short Answer

Expert verified

(a) The velocity of the wind relative to earth is-4m/s.

(b) The time taken when the bird is moving with the wind will be 7.7 min.

(C) Due to wind, bird takes (20 鈥� 7.7) min less time compared with no wind.

Step by step solution

01

Definition of velocity

The directional speed of an item in motion is an indication of its rate of change in position as seen from a specific point of view and measured by a specific time standard.

02

Given data

The velocity can be said as Vi is9.0m/s The velocity is making some angle with the x axis.

The bird travels in x direction is6km that is distance in meter =6000meter

The time taken by bird is20min, which can be converted into seconds

t = 20 x 60 = 1200 s

The velocity of the bird relative to the wind is Vbw 9m/s

The gravitational acceleration is-9.8m/s2

03

Velocity of the bird opposite to wind

The velocity of the bird

Vb-=xtVb-=60001200Vb-=5m/s

The velocity of the bird relative to earth is 5 m/s.


a. The velocity of the wind will be

Vwe=Vwb+VbeVwe=-9+5Vwe=-4m/s

The velocity of the wind relative to earth is -4 m/s.


04

Time of the bird to return 6 km with the direction of wind

b. Time of the bird to return 6 km with the direction of wind is

Vbe炉=xet

The velocity of the bird relative to the earth

Vbe=Vbw+VweVbe=-9+-4Vbe=-13m/s


Putting the value of velocity in the equation

Vbe-=Xet-13=-6000tt=600013t=462s=7.7min

The time taken when the bird is moving with the wind will be 7.7 min .


(C) Due to wind, bird takes (20 鈥� 7.7) min less time compared with no wind.

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Most popular questions from this chapter

Suppose a pilot flies40.0kmin a direction60掳 north of east and then flies in a direction role="math" localid="1668679997174" 15掳north of east as shown in Figure 3.63. Find her total distance Rfrom the starting point and the direction 胃of the straight-line path to the final position. Discuss qualitatively how this flight would be altered by a wind from the north and how the effect of the wind would depend on both wind speed and the speed of the plane relative to the air mass.

An arrow is shot from a height of \(1.5{\rm{ m}}\) toward a cliff of height \(H\). It is shot with a velocity of \(30{\rm{ m}}/{\rm{s}}\) at an angle of \(60^\circ \) above the horizontal. It lands on the top edge of the cliff \(4.0{\rm{ s}}\) later.

(a) What is the height of the cliff?

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(a) Repeat the problem two problems prior, but for the second leg you walk \(20.0{\rm{ m}}\) in a direction \(40.0^\circ \) north of east (which is equivalent to subtracting \({\rm{B}}\) from \({\rm{A}}\) 鈥攖hat is, to finding \({\rm{R'}} = {\rm{A}} - {\rm{B}}\)).

(b) Repeat the problem two problems prior, but now you first walk \(20.0{\rm{ m}}\) in a direction \(40.0^\circ \) south of west and then \(12.0{\rm{ m}}\) in a direction \(20.0^\circ \) east of south (which is equivalent to subtracting \({\rm{A}}\) from \({\rm{B}}\) 鈥攖hat is, to finding \({\rm{R''}} = {\rm{B}} - {\rm{A}} = - {\rm{R'}}\)). Show that this is the case.

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