To show derivations of the function of the form f(x,y,z)with
many independent variables is impossible for
non-holonomicconstraints involved.i tried 6 equations to prove but
wantcorrection if possible.

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Ответ:

neariah24

06.06.2022

Physics

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 . 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 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 , , and :

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

Apply this equation to find the value of :

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

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 $2\times 36.45\; \rm m = 72.9\; \rm m$ .

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To show derivations of the function of the form f(x,y,z)with many independent variables is impossible for non-holonomicconstraints involved.i tried 6 equations to prove but wantcorrection if possible.