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Suppose a pilot flies 40.0 km in a direction 60º north of

Chapter 3, Problem 24

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QUESTION:

Suppose a pilot flies \(40.0 km\) in a direction \(60^{\circ}\) north of east and then flies \(30.0 km\) in a direction \(15^{\circ}\) north of east as shown in Figure \(3.63\). Find her total distance \(R\) from the starting point and the direction \(\theta\) 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.

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QUESTION:

Suppose a pilot flies \(40.0 km\) in a direction \(60^{\circ}\) north of east and then flies \(30.0 km\) in a direction \(15^{\circ}\) north of east as shown in Figure \(3.63\). Find her total distance \(R\) from the starting point and the direction \(\theta\) 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.

ANSWER:

 

Step 1 of 6 :

In this question, we need to find the direction and magnitude of the resultant vector 

Condition given for resultant 

\(R=A+B\)

We also need to quantitatively how wind from north can alter the flight, and the effect depends on speed of plane and relative air mass 

Data given:

 \(A=40 \mathrm{~km}\)

\(B=30 \mathrm{~km}\)

\(\theta_{A}=60^{\circ}\)

\(\theta_{B}=15^{0}\)

Considering given figure 

 

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