Introduction:
We are given that a body is thrown vertically upward with a certain velocity and reaches a maximum height of 100 meters. We are also given that another body, which is twice the mass of the first body, is thrown upward with a velocity twice that of the first body. We need to find the maximum height reached by the second body.

Key Information:
- Initial velocity of the first body: v
- Initial velocity of the second body: 2v (twice the velocity of the first body)
- Maximum height reached by the first body: 100 meters

Analysis:
When a body is thrown vertically upward, it experiences a constant acceleration due to gravity in the opposite direction of its motion. This acceleration is equal to the acceleration due to gravity, denoted by 'g', and has a value of approximately 9.8 m/s².

Using the equations of motion, we can determine the time taken for the first body to reach its maximum height and the time taken for it to reach the ground again. Since the initial velocity is in the upward direction, the final velocity at the maximum height is 0 m/s.

Calculations:
1. To find the time taken to reach the maximum height by the first body:
Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken, we have:
0 = v - gt
t = v/g

2. To find the time taken to reach the ground by the first body:
Using the equation v = u + at, where v is the final velocity and u is the initial velocity, we have:
0 = v - gt
t = v/g

3. To find the time taken to reach the maximum height by the second body:
Using the equation v = u + at, where v is the final velocity and u is the initial velocity, we have:
0 = 2v - gt
t = 2v/g

Result:
The time taken by the second body to reach its maximum height is given by t = 2v/g. Since the initial velocity of the second body is twice that of the first body, we have 2v = 2u = 4v. Substituting this value in the equation, we get:
t = 4v/g

Therefore, the time taken by the second body to reach its maximum height is four times the time taken by the first body. As the time taken by the first body to reach its maximum height is the same as the time taken to reach the ground, the time taken by the second body to reach its maximum height is also four times the time taken to reach the ground. Hence, the maximum height reached by the second body can be calculated by multiplying the maximum height reached by the first body by four.

Conclusion:
The maximum height reached by the second body is four times the maximum height reached by the first body. Therefore, the maximum height reached by the second body is 400 meters.

The 2nd body will reach a maximum height of 400m ........use, v²-u²=2gh........ to get the answer.....