Question

A plane is flying at a height of 5000 m above the sea level. At a particular point, it is exactly above a submarine floating 1200m below sea level. What is the vertical distance between them?

Answer 1

Hint: We have been given the height of the plane flying from the sea level, therefore we need to understand the concept of height and distance to solve this question. Since this is a simple question it does not involve the concept of angle of elevation and depression.

Complete step-by-step answer:
Another application in finding height and distance is the direction. Therefore we will be taking into consideration the direction. Suppose the point where the aeroplane flying above the sea level comes directly above the submarine floating below is A. distance of this point A from the sea level is given by 5000m.

Let the point at which submarine is directly under the aeroplane be point B. when the distance of the submarine from the sea level is given as 1200m.
Therefore the distance to be calculated is supposed to be given by the distance between A and B by the length of AB.
Since we are well aware of the positions of aeroplane and submarine now, we need to understand the direction for that suppose the sea level is the level zero and the direction of the aeroplane is north to it which is upward and the direction of submarine is downward that is in the south direction.
If the distance while going upward in north direction is taken as positive then the distance while going in south has to be taken as negative, therefore
Distance OA=+5000m
Distance OB=-1200m
\[
\Rightarrow {Distance{\text{ }}AB = \left| {OA} \right| + \left| {OB} \right|} \\
  {AB = \left| { + 5000} \right| + \left| {\left( { - 1200} \right)} \right|} \\
  {AB = 5000 + 1200 = 6200m}
\]
Therefore 6200m is the vertical distance between aeroplane and submarine.

Note: We must be careful because though the direction is taken care of and it affects the magnitude of the distance by changing its sign accordingly but the distance is a positive quantity always as it is the absolute value of the displacement.