Question

Copenhagen is located 780 km North and 810 km East of Paris. A flight from Paris to Copenhagen takes two hours. Typically the wind blows from East to West over Europe, but the speed varies. For one particular flight, the wind speed was 165 km/h. What is the magnitude of vpa, the plane's velocity with respect to the air

Answer 1

`V_(pa)=690km/hr`

Step-by-step explanation:

In order to solve this problem, we can start by drawing a diagram of what the problem looks like. (See attached picture).

We can treat this as a vector problem, so we can start by finding the velocities of the plane with respect to the earth as it goes north and east. Velocity is found by using the following formula:

`Velocity=(distance)/(time)`

so

`V_(paN)= (780km)/(2hr)`

`V_(paN)=390 km/hr`

Since air isn't affecting the north direction of the plane, we will keep this as the velocity due north.

Now let's find the velocity of the plane with respect to the earth towards the east:

`V_(pE)=(810km)/(2hr)`

`V_(pE)=405 km/hr`

In this case, since the wind is blowing from east to west, then it affects directly the velocity of the plane with respect to the earth, so we can use the following formula to determine the Velocity of the plane with respect to the air in the eastern direction:

`V_(paE)-V_(a)=V_(pE)`

so we can solve this for the velocity of the plane on the air towards the east, so we get:

`V_(paE)=V_(pE)+V_(a)`

so we get:

`V_(paE)=405 km/hr + 165km/hr`

`V_(paE)=570 km/hr`

So now we can use this data to find the velocity of the plane with respect to the air:

`V_(pa)=\sqrt{V_(paN)^(2)+V_(paE)^(2)}`

so we get:

`V_(pa)=\sqrt{(390km/hr)^(2)+(570km/hr)^(2)}`

`V_(pa)=690.65 km/hr`