Question

4. A group of students made a rocket and launched it vertically upwards with velocity

Answer 1

Answer:

Approximately $72.9\; \rm m$, assuming that the rocket had no propulsion onboard, and that air resistance on the rocket is negligible.

Explanation:

Initial velocity of this rocket: $u = 27\; \rm m\cdot s^{-1}$.

When the rocket is at its maximum height, the velocity of the rocket would be equal to $0$. That is: $v = 0\; \rm m \cdot s^{-1}$.  

The acceleration of the rocket (because of gravity) is constantly downwards, with a value of $a = -g = -10\; \rm m \cdot s^{-2}$.

Let $x$ denote the distance that the rocket travelled from the launch site to the place where it attained maximum height. The following equation would relate $x \!$ to $u$, $v$, and $a$:

$\displaystyle x = \frac{v^2 - u^2}{2\, a}$.

Apply this equation to find the value of $x$:

$\begin{aligned} x &= \frac{v^2 - u^2}{2\, a} \\ &= \frac{\left(0\; \rm m\cdot s^{-1}\right)^{2} - \left(27\; \rm m \cdot s^{-1}\right)^{2}}{2 \times 10\; \rm m \cdot s^{-2}} = 36.45\; \rm m\end{aligned}$.

In other words, the maximum height that this rocket attained would be $36.45\; \rm m$.

Again, assume that the air resistance on this rocket is negligible. The rocket would return to the ground along the same path, and would cover a total distance of $2\times 36.45\; \rm m = 72.9\; \rm m$.