Respuesta :
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.
[tex]v_p = v_p_/_a + v_a[/tex]
- The velocity of plane (vp) is:
[tex]v_p = 500 + 60\\\\v_p = 560 mph[/tex]
- The distance between LA and London is ( d ) is travelled by the aeroplane in time:
[tex]t_1 = \frac{d}{v_p}[/tex]
- Determine the time (t1) for LA to London journey:
[tex]t_1 = \frac{5,000}{560}\\\\t_1 = 8.92857 hr[/tex]
- 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.
[tex]v_p = v_p_/_a + v_a[/tex]
- The velocity of plane (vp) is:
[tex]v_p = 500 - 60\\\\v_p = 440 mph[/tex]
- The distance between LA and London is ( d ) is travelled by the aeroplane in time:
[tex]t_2 = \frac{d}{v_p}[/tex]
- Determine the time (t2) for London to LA journey:
[tex]t_2 = \frac{5,000}{440}\\\\t_2 = 11.3636363 hr[/tex]
- We see that the return journey from London to LA takes (t2) hours which is :
[tex]dt = t_2 - t_1\\\\dt = 11.3636364 - 8.92857\\\\dt = 2.435 hrs[/tex]
Answer: dt = 2.435 hours more than the journey from LA to London.
