Question

A transcontinental flight of 4680 km is scheduled to take 43 min longer westward than eastward. The airspeed of the airplane is 970 km/h, and the jet stream it will fly through is presumed to move due east. What is the assumed speed of the jet stream?

Answer 1

The assumed speed of the jet stream is 43.33 km/h.

Step-by-step explanation:

To find the speed of the jet stream, we need to use the concept of relative velocity. Let's assume that the eastbound speed of the airplane (with no wind) is ve, and the westbound speed is vw. Since the flight eastward takes 43 minutes less, we can write the following equation:

ve = vw + 43/60

We know that the airspeed of the airplane is 970 km/h, which is equal to ve + vj, where vj is the speed of the jet stream. Substituting the values, we get:

970 = vw + 43/60 + vj

Now, we can use the given information that the jet stream is moving due east to relate the speeds:

ve = vw - vj

Substituting the value of ve, we get:

970 = vw + 43/60 - vj

From these two equations, we can solve for vw and vj. Solving them simultaneously, we find vw = 463 and vj = 43/60. Therefore, the assumed speed of the jet stream is 43/60 km/h or approximately 43.33 km/h.

Answer 2

To solve this problem we will apply the concepts related to speed as a function of distance and time (This time will be cleared to find a function that fits the requirement of the problem) and the net velocity of the object. From these considerations an equation will be generated that allows to find the speed of the jet. If the plane is moving in eastward, the ground speed is

`v_(gs) = v_(as) +v_(js)`

So the time is

`t_1 = (d)/(v_(as)+v_(js))`

If the plane is moving in westward, the ground speed is,

`v_(gs) = v_(as) -v_(js)`

So the time is

`t_2 = (d)/(v_(as)-v_(js))`

The time difference is

`t_2-t_1 = v_(as) -v_(js) - (d)/(v_(as)+v_(js))`

`t_2-t_1 = (2dv_(js))/(v_(as)^2-v_(js)^2)`

`43min (1h)/(60min) = (2dv_(js))/(v_(as)^2-v_(js)^2)`

`(43)/(60) = (2dv_(js))/(v_(as)^2-v_(js)^2)`

`43v_(as)^2-43v_(js)^2 = 120dv_(js)`

From the above equation the speed of the jet stream is

`43(970km/h)^2 -43v_(js)^2 = 120(4680)v_(js)`

`40.45*10^6km^2/h^2 -43v_(js)^2-561600v_(js) = 0`

`v_(js) = 71.6335m/s`

Therefore the assumed speed of the jet stream is 71.63m/s