Two cars are moving along intersecting roads at right angles: one at a speed of 54 km / h

| February 19, 2021 | education

Two cars are moving along intersecting roads at right angles: one at a speed of 54 km / h to the east, the other at a speed of 72 km / h to the north. How many seconds after they meet at the intersection, the distance between them will become equal to 625 m?

Data: α (angle between vectors of speeds of specified machines) = 90º; V1 (speed of the first car) = 54 km / h (in SI V1 = 15 m / s); V2 (speed of the second car) = 72 km / h (in SI V2 = 20 m / s); S (required distance) = 625 m.

The time elapsed after the meeting of the given machines is determined by the Pythagorean theorem: S ^ 2 = S1 ^ 2 + S2 ^ 2 = (V1 * t) ^ 2 + (V2 * t) ^ 2 = t ^ 2 * (V1 ^ 2 + V2 ^ 2), whence t ^ 2 = S ^ 2 / (V1 ^ 2 + V2 ^ 2) and t = √ (S ^ 2 / (V1 ^ 2 + V2 ^ 2)).

Let’s perform the calculation: t = √ (625 ^ 2/15 ^ 2 + 20 ^ 2)) = √ (625 ^ 2/625)) = √625 = 25 s.



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