Physics: One of the signs a chemical reaction is taking place

One of the signs a chemical reaction is taking

Ответ:

Vlop3971

22.05.2022

Vertical displacement when t=t_r is $\b{\boxed{\sqrt{2gH}\left(t\right)-\dfrac{1}{2}g{t^2}}}$ and vertical displacement when ${t_r}$ is $\b{\fbox{\begin\{t({\sqrt{2gH}+\dfrac{g(t_r-2t)}{2})}\end{minispace}}}$ .

Further Explanation:

Arabella and Boris are of same height and jumps with the same initial velocity. Therefore, both can jump to height .

The energy of both the players Arabella and Boris at ground level and height is constant.

Concept:

Applying conservation of energy at ground and height :

$mgH=\dfrac{1}{2}m{v_0}^2$

Rearrange the above equation for initial velocity v_0 :

$v_0=\sqrt{2gH}$

To calculate the height of both players, we can apply the equation of law of motion.

For a given initial velocity v_0 , acceleration , the height of the Arabella in time :

$\boxed{{h_a}\left(t\right) ={h_0}+{v_0}t-\dfrac{1}{2}g{t^2}}$

The reaction time for Boris is t_r . Therefore, to reach the height time taken by her is (t-t_r) .

For a given initial velocity v_0 , acceleration , the height of the Boris in time (t-t_r) :

$\boxed{{h_b}(t)={h_0}+{v_0}(t-t_r)+\dfrac{1}{2}g(t-t_r)^2}$

It is given that Boris jumps before Arabella reaches the maximum height. Therefore, reaction time for Boris cannot be greater than total time.

Case I:

For t=t_r , we get ${h_b}(t)={h_0}$ .

Therefore, the vertical displacement is:

$\begin{aligned}D(t)&={h_a}(t)-{h_b}(t)\\&={h_0}+{v_0}t-\dfrac{1}{2}g{t^2}-{h_0}\\&={v_o}t-\dfrac{1}{2}g{t^2}\\&=\sqrt{2gH}(t)-\dfrac{1}{2}g{t^2}\end{gathered}$

Case II:

For ${t_r}$ , the vertical displacement is:

$\begin{aligned}D(t)&={h_a}(t)-{h_b}(t)\\&={t_r}({\sqrt{2gH}+\dfrac{g(t_r-2t}{2})\end{aligned}$

Thus, vertical displacement when t=t_r is $\b{\boxed{\sqrt{2gH}\left(t\right)-\dfrac{1}{2}g{t^2}}}$ and vertical displacement when ${t_r}$ is $\b{\fbox{\begin\{t({\sqrt{2gH}+\dfrac{g(t_r-2t)}{2})}\end{minispace}}}$ .

Learn more:

1. Average translational kinetic energy:

2. Stress on a body under tension:

3. Water is a compound:

Answer Details:

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords:

Two, basketball, player, same, height, initial, velocity, vertical, distance, Arabella, Boris, high, above, D(t)=Ha(t) – Hb(t), function, reaction, ground, reaches and time.

Two basketball players are essentially equal in all respects. (they are the same height, they jump w

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One of the signs a chemical reaction is taking place

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