Chapter 4: Q137P (page 93)

A transcontinental flight of4350 km is scheduled to take 50 minlonger westward than eastward. The airspeed of the airplane is 966 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?

Short Answer

Expert verified

Speed of Jet Streamis 88.63 km/h .

Step by step solution

The given data

Length of transcontinental flight, $D = 4350 km$ .
Extra time that will be taken by the flight, $v_{f l i g h t} = 966 km / h$ .
Airspeed of the airplane, $t_{1} - t_{2} = 50 \min or 5 / 6 h$ .

Understanding the concept of relative velocity

When there is a relative motion at a constant velocity between the two frames of reference, frameAand frame B, the velocity of a particle Pas measured by an observer in frame Ais different than the velocity of a particle P measured in frame B. The relation between two velocities is given as,

${\vec{v}}_{P A} = {\vec{v}}_{P B} + {\vec{v}}_{B A}$

Here ${\vec{v}}_{BA}$ is the velocity of B with respect to A.

Use the concept of relative velocity to find the jet stream.

Formula:

The velocity of a body in motion, $v = \frac{d}{t}$ (i)

is velocity, $d$ is distance, $t$ and is time for the motion.

Calculation of the speed of the jet stream

It is given that the westward plane is taking longer than that of the eastward. Hence, the time difference as given:

$t_{1} - t_{2} = \frac{5}{6} h$

Substitute the equation for time and simplify it.

$\frac{D}{966 k m / h - v} - \frac{D}{966 k m / h + v} = \frac{5}{6} \frac{4350 k m}{966 - v} - \frac{4350 k m}{966 + v} = \frac{5}{6} 4350 (\frac{1}{966 - v} - \frac{1}{966 + v}) = \frac{5}{6} \frac{4350 ((966 - v) - (966 - v))}{960^{2} - v^{2}} = \frac{5}{6}$