Two cars are driving on mutually perpendicular roads. The first car approaches the intersection

Two cars are driving on mutually perpendicular roads. The first car approaches the intersection with a speed, the modulus of which is v1 = 72 km / h, the second one moves away from it with a speed, the modulus of which is v2 = 54 km / h. At the initial moment of time, the first car is at a distance of l1 = 290m, and the second – at a distance of l2 = 95m from the intersection. After what time interval will the distance between the cars be the same as at the initial moment of time?

Let the time when the distance remains the same will be t. First, let’s determine the initial distance between cars:

(l0) ^ 2 = (l1) ^ 2 + (l2) ^ 2 = 290 ^ 2 + 95 ^ 2 = 84100 + 9025 = 93125 (m).

Let’s translate the speed into m / s: v1 = 72 km / h = 72 * (1000/3600) m / s = 20 m / s); v2 = 54 km / h = 54 * (1000 /) m / s) = 15 m / s.

Let’s make an equation for time t:

(290 – 20 * t) ^ 2 + (95 + 15 * t) ^ 2 = (l0) ^ 2 = 93125; we solve for t: 290 ^ 2 – 2 * 20 * 290 + 400 * t ^ 2 + 95 ^ 2 + 95 * 30 * t + 225 * t ^ 2 = 93125; After transformation we get:

25 * t ^ 2 – 8 ^ 58 * t + 6 * 19 ^ t = 0; t = 14 (c)