Question

The height of both the towers is 50m. The length of the rope is 80m. The rope is tied from the top of the first tower to the top of the second tower. Now the minimum distance between rope and ground is 10m. Find the distance between two towers in meters.

Answer 1

Hint: Now we are given that the height of the tower is 50m. The minimum distance between rope and ground is 10m. Now, this minimum distance occurs at the midpoint of the rope. Hence we can find the distance of the rope before this point. Now also calculate the vertical distance between the top of the tower and the minimum point. This shall give the answer to the question.

Complete step-by-step solution

Now consider the rope that is suspended from the top of tower 1 to tower 2 each of length 50m
The length of rope is given as 80m.
Now consider the point where the rope is at a minimum distance from the ground.
We know that this distance will occur at the midpoint of rope as well as the midpoint of horizontal distance between towers.
Now since the length of rope is 80m the length of rope before this point is $\dfrac{80}{2}=40m$
Now we have the length of rope suspended before mid-point is 80m …………….. (1)
Now consider the tower.
The height of the tower is 50m
Now we check the vertical distance of rope from the midpoint.
This distance is the height of the tower – the height of rope from the ground at this point
$= 50 – 10 = 40m $
Hence we have the vertical distance of midpoint of rope and top of the tower is $40m$ ……….. (2)
Now from (1) and (2), we can say that the rope is suspended straight, and hence the distance between towers must be 0m
Hence the distance between towers is 0m

Note: Note that in this problem there is no way that we can find the circumference of rope and height of towers. Hence for such problems always try to analyze the given data to find the answer.