Problem 24PE

Suppose a pilot flies 40.0 km in a direction 60º north of east and then flies 30.0 km in a direction 15º north of east as shown in Figure 3.63. Find her total distance R from the starting point and the direction θ 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.

Problem 24PE

Solution 24PE

Step 1 of 6 :

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

Condition given for resultant

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

Considering given figure

Step 2 of 6 :

From the figure we understand that we need to find the resultant vector

Case 1 :

We shall find x and y component to vector A

It is given by

Substituting values we get

Similarly y component is given by

Substituting values we get

Thus we have component as and component as

Case 2:

We shall find x and y component to vector B

It is given by

Substituting values we get

Similarly y component is given by

Substituting values we get

Thus we have component as and component as

Step 3 of 6 :

Now we shall find components of resultant vector

Case 3:

We get component of resultant vector as

Substituting values we get

Case 4 of 6 :

We get component of resultant vector as

Substituting values we get

Thus we have components of resultant vector as and