Wind drift

A plane flies at 780 km/h airspeed. It covers a distance of 1200 km with the wind and then the same distance against the wind in a total of 3 h 5 min. What is the wind speed?

Final Answer:

w = 35.5649 km/h

Step-by-step explanation:

v = 780 km/h a = 1200 km T = 3 : 5 = 3 h r 5 m i n = 3 + \frac{5}{6 0} = 3.0833 h r ≐ 3.0833 t_{1} + t_{2} = T (v + w) t_{1} = a (v - w) t_{2} = a (v + w) t_{1} = a (v - w) (T - t_{1}) = a (v - w) (T - \frac{a}{v + w}) = a (v - w) \cdot (T \cdot (v + w) - a) = a \cdot (v + w) (780 - w) \cdot (3.0833333333333 \cdot (780 + w) - 1200) = 1200 \cdot (780 + w) - 3.0833333331393 w^{2} + 3900 = 0 3.0833333331393 w^{2} - 3900 = 0 w_{1, 2} = \pm 3899.99999998 / 3.0833333331393 = \pm 35.564938703 w_{1} = 35.564938703 w_{2} = - 35.564938703 w = w_{1} = 35.5649 ≐ 35.5649 km/h t_{1} = \frac{a}{v + w} = \frac{1 2 0 0}{7 8 0 + 3 5 . 5 6 4 9} ≐ 1.4714 h t_{2} = \frac{a}{v - w} = \frac{1 2 0 0}{7 8 0 - 3 5 . 5 6 4 9} ≐ 1.612 h Verifying Solution: a_{1} = (v + w) \cdot t_{1} = (780 + 35.5649) \cdot 1.4714 = 1200 km a_{2} = (v - w) \cdot t_{2} = (780 - 35.5649) \cdot 1.612 = 1200 km T_{2} = t_{1} + t_{2} = 1.4714 + 1.612 = \frac{3 7}{1 2} ≐ 3.0833 h

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You need to know the following knowledge to solve this word math problem:

algebra

Units of physical quantities

themes, topics

motion problems

Grade of the word problem

high school

Wind drift

Final Answer:

Step-by-step explanation:

You need to know the following knowledge to solve this word math problem:

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