Problem:
A body is dropped from the top of a tower. It covers a distance 7x in the last second of its journey, where x is the distance covered in the first second. How much time will it take to reach the ground?

Solution:

Step 1: Understand the problem
When a body is dropped from a certain height, it gains velocity due to gravitational pull and its speed increases as it falls. The distance covered by the body in the first second is x, and the distance covered in the last second is 7x. We need to find the total time taken by the body to reach the ground.

Step 2: Use equations of motion
We can use the equations of motion to solve this problem. The equation for distance covered by a body in free fall is given by:

s = ut + 1/2 at^2

Where s is the distance covered, u is the initial velocity (which is zero in this case), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time taken.

Using this equation, we can find the time taken by the body to cover the distance x in the first second:

x = 1/2 * (-9.8) * t^2

Simplifying this equation, we get:

t = √(2x/9.8)

Similarly, we can find the time taken by the body to cover the distance 7x in the last second:

7x = 1/2 * (-9.8) * (t-1)^2

Simplifying this equation, we get:

t = 1 + √(14x/9.8)

Step 3: Calculate the total time taken
The total time taken by the body to reach the ground is the sum of the time taken in the first second and the time taken in the last second:

Total time = t + (t-1)

Substituting the values of t in these equations, we get:

Total time = √(2x/9.8) + 1 + √(14x/9.8) - 1

Simplifying this equation, we get:

Total time = √(2x/9.8) + √(14x/9.8)

Step 4: Final answer
Therefore, the time taken by the body to reach the ground is √(2x/9.8) + √(14x/9.8).