COLLEGE PHYSICS-CONNECT ACCESS
COLLEGE PHYSICS-CONNECT ACCESS
5th Edition
ISBN: 9781260486834
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 3, Problem 86P

(a)

To determine

The change of direction requires compensating for the wind.

(a)

Expert Solution
Check Mark

Answer to Problem 86P

The change of direction requires compensating for the wind is 9.45north of west.

Explanation of Solution

In this case, let x in the east direction and y in the north direction.

Air speed of the small plane is 30m/s and wind blowing is 10m/s,30south of west.

Write the expression forthe airspeed of the small plane,

  vPA=vPAcosθx^+vPAsinθy^        (I)

Here, vPA is the airspeed of the small plane, vPA is the velocity of the plane relative to the air and θ is the change of direction.

Write the expression forthe wind flow,

  vAG=vAGcosϕx^+vAGsinϕy^        (II)

Here, vAG is the wind flow, ϕ is the change in angle and vAG is the velocity of the air relative to the ground.

In this case,

    (vPA)y+(vAG)y=0        (III)

Conclusion:

Substitute 30m/s for vPA in (I),

  vPA=30cosθx^+30sinθy^

Substitute 10m/s for vAG and 30 for θ in (II),

  arad=10m/scos30x^10m/ssin30y^=(8.66x^5y^)m/s

Substitute 30sinθ for (vPA)y and 5 for (vAG) in (III),

    30sinθ+(5)=0sinθ=530θ=sin1(16)=9.45northofeast

Therefore, the change of direction requires compensating for the wind is 9.45north of west.

(b)

To determine

The ground speed of the airplane after she changes the direction of the heading.

(b)

Expert Solution
Check Mark

Answer to Problem 86P

The ground speed of the airplane is 38.26m/s.

Explanation of Solution

From the part (a) equation (I),

    vPA=vPAcosθx^+vPAsinθy^

Write the expression for the velocity of the plane relative to the ground.

    |vPG|=|(vPA)x|+|(vAG)x|        (IV)

Conclusion:

Substitute 9.45 for θ and 30m/s for vPA in equation (I) from part (a)

    vPA=30cos9.45x^+30sin9.45y^=(29.6x^+4.9y^)m/s

Substitute 8.66m/s for (vPA)x and 29.6m/s for (vAG)x in (IV),

    |vPG|=|8.66m/s|+|29.6m/s|=38.26m/s

Therefore, the ground speed of the airplane is 38.26m/s.

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Chapter 3 Solutions

COLLEGE PHYSICS-CONNECT ACCESS

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