Question

An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1 1/2 hours?

(A) 300√67 km

(B) 400√61 km

(C) 200√61 km

(D) 300√61 km

Answer 1

The correct option is: (D) 300√61 km

Explanation:

Let the point A represent the airport.

Let the plane-I fly towards North.

.'. Distance of the plane-I from the airport after 1 1/2 hours

Let the plane-II fly towards West.

.'. Distance of the plane-II from the airport after 1 1/2 hours

Now, in right ΔABC, using Pythagoras theorem, we have

Thus, after 1 1/2 hours, the two planes will be 300√61 km apart from each other.