The balloon rises relative to the Earth to a certain height and is simultaneously

The balloon rises relative to the Earth to a certain height and is simultaneously blown by the wind at a distance of 0.6 km in the horizontal direction. To what height did the ball rise if its movement is 1 km?

Given:

L = 0.6 kilometers = 600 meters – the horizontal distance to which the balloon was carried by the wind;

S = 1 kilometer = 1000 meters – the movement of the balloon.

It is required to determine H (meters) – the height to which the balloon has risen.

According to the condition of the problem, the motion of the ball is rectilinear. The balloon moved in two directions: vertically and horizontally. Then, its movement is the hypotenuse of a right-angled triangle, and by the Pythagorean theorem:

S ^ 2 = L ^ 2 + H ^ 2;

H ^ 2 = S ^ 2 – L ^ 2;

H = (S ^ 2 – L ^ 2) ^ 0.5 = (1000 ^ 2 – 600 ^ 2) ^ 0.5 = (1,000,000 – 360,000) ^ 0.5 = 640,000 ^ 0.5 = 800 meters.

Answer: the ball has risen to a height of 800 meters.