Question

A plane has an average air speed (this is the speed the plane moves through air) of 500mph. The plane flies a route of 5,000miles from Los Angeles to London. The average speed of the wind along this route is 60mph blowing east from Los Angeles towards London. How much longer does it take the plane to fly from London to Los Angeles than the reverse direction?

Answer 1

Answer:

2.435 hrs

Step-by-step explanation:

Given:-

- The average speed of airplane relative to air, vp/a = 500 mph

- The average speed of wind, va = 60 mph

- The wind direction = LA to London

- The distance between LA and London, d = 5,000 miles

Find:-

How much longer does it take the plane to fly from London to Los Angeles than the reverse direction?

Solution:-

- We will take all directions in east as positive. The best way to deal with such questions is to determine the vector quantities ( velocity ) in the stationary frame.

- Taking the journey from LA to London. The aeroplane has a relative velocity of vp/a = +500 mph and the wind blows in the same direction as the velocity of aeroplane i.e va = +60 mph.

- To determine the true velocity of the plane relative to any stationary frame on the ground our vector equation becomes.

                                  $v_p = v_p_/_a + v_a$

- The velocity of plane (vp) is:

                                    $v_p = 500 + 60\\\\v_p = 560 mph$

- The distance between LA and London is ( d ) is travelled by the aeroplane in time:

                                    $t_1 = \frac{d}{v_p}$

- Determine the time (t1) for LA to London journey:

                                $t_1 = \frac{5,000}{560}\\\\t_1 = 8.92857 hr$

- Taking the journey from London to LA. The aeroplane has a relative velocity of vp/a = +500 mph and the wind blows in the opposite direction as the velocity of aeroplane i.e va = -60 mph.

- To determine the true velocity of the plane relative to any stationary frame on the ground our vector equation becomes.

                                  $v_p = v_p_/_a + v_a$

- The velocity of plane (vp) is:

                                    $v_p = 500 - 60\\\\v_p = 440 mph$

- The distance between LA and London is ( d ) is travelled by the aeroplane in time:

                                    $t_2 = \frac{d}{v_p}$

- Determine the time (t2) for London to LA journey:

                                $t_2 = \frac{5,000}{440}\\\\t_2 = 11.3636363 hr$

- We see that the return journey from London to LA takes (t2) hours which is :

                                 $dt = t_2 - t_1\\\\dt = 11.3636364 - 8.92857\\\\dt = 2.435 hrs$

Answer: dt = 2.435 hours more than the journey from LA to London.