Question

A light airplane flies north at 250 km/hr. at the same time, another airplane starts from an airport 140 km north of the first airplane and is travelling east at 300 km/hr. what is the closest distance (to the nearest kilometer) that the two airplanes ever approach each other?

Answer 1

The closest distance that the two airplanes ever approach each other is approximately 390.52 km/hr.

Step-by-step explanation:

To find the closest distance that the two airplanes ever approach each other, we can consider their relative motion. One airplane is flying north at 250 km/hr and the other is flying east at 300 km/hr. We can break down their velocities into vertical and horizontal components. The first airplane's vertical component is 250 km/hr and the second airplane's horizontal component is 300 km/hr.

Using the Pythagorean theorem, we can find the resultant velocity, which is the closest distance the two airplanes approach each other. The resultant velocity is the hypotenuse of a right triangle formed by the two component velocities. The hypotenuse can be calculated as √(250^2 + 300^2) = √(62500 + 90000) = √152500 ≈ 390.52 km/hr.

Therefore, the closest distance that the two airplanes ever approach each other is approximately 390.52 km/hr.