A roket fired vertically ascends with a constant acceleration `g//3` for `1 min`. Its fuel is then all used and it continues to rise as a free body. What is the maximum height reached? What is the total time elapsed from the take off until the rocket strikes the earth?

Explanation

To solve the problem, we will break it down into steps:

### Step 1: Calculate the velocity of the rocket after 1 minute of acceleration
The rocket accelerates with a constant acceleration of \( \frac{g}{3} \) for 1 minute (which is 60 seconds).

Using the formula for velocity under constant acceleration:
\[
v = u + at
...