Two balls of masses 2 m and 6 m are thrown in air : one vertically upwards and other at an angle `theta` with the vertical . The balls remain in air for the same time . Find the ratio of maximum heights attained by them.

Explanation

To solve the problem, we need to find the ratio of the maximum heights attained by two balls thrown in the air: one vertically upwards and the other at an angle θ with the vertical. Let's denote the masses of the balls as 2m and 6m, respectively, but note that the mass does not affect the maximum height in this case.

### Step-by-Step Solution:

1. **Determine the time of flight for the first ball (mass 2m thrown vertically upwards):**
- The time of flight \( T_1 \) for an object thrown vertically upwards with initial velocity \( u \) is given by:
\[
T_1 = \frac{2u}{g}
...