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11P

Expert-verifiedFound in: Page 78

Book edition
9th Edition

Author(s)
Raymond A. Serway, John W. Jewett

Pages
1624 pages

ISBN
9781133947271

**Mayan kings and many school sports teams are named for the puma, cougar, or mountain lion****Felis concolor**** the best jumper among animals. It can jump to a height of $\mathbf{12}.\mathbf{0}\text{}\mathbf{ft}$****when leaving the ground at an angle of $\mathbf{45}.\mathbf{0}\xb0$****. With what speed, in ****units, does it leave the ground to make this leap?**

** **

The initial velocity of the speed is ${v}_{i}=12\text{m}/\text{s}$.

** **

- The initial velocity, denoted by $u$, is the velocity at time interval $t=0$. It's the speed at which the motion begins.
- The starting velocity is articulated as $u=v-at$ if time, acceleration, and final velocity are provided.
- Where $u$ is the initial velocity , $v$ is the final velocity,is the time taken, and $a$ is the acceleration

Given data,

${y}_{\mathrm{max}}=12\text{ft}\phantom{\rule{0ex}{0ex}}{y}_{\mathrm{max}}=\frac{12}{3.28}\phantom{\rule{0ex}{0ex}}{y}_{\mathrm{max}}=3.66\text{m}\phantom{\rule{0ex}{0ex}}$

First, we need to find the time required to reach this height which we get by using this equation:

${v}_{yf}={v}_{yi}+{a}_{y}t$

Solving $t$ for taking into account that at the maximum height ${v}_{y}=0$ and $a=-g:$

$t=\frac{{v}_{yf}-{v}_{yi}}{{a}_{y}}\phantom{\rule{0ex}{0ex}}t=\frac{0-{v}_{yi}}{-g}\phantom{\rule{0ex}{0ex}}t=\frac{{v}_{yi}}{g}$

Then, we need to find the vertical displacement made in this time by using the following equation:

${y}_{\mathrm{max}}={v}_{y,avg}t\phantom{\rule{0ex}{0ex}}{y}_{\mathrm{max}}=\left(\frac{{v}_{yi}+{v}_{yf}}{2}\right)t\phantom{\rule{0ex}{0ex}}{y}_{\mathrm{max}}=\left(\frac{{v}_{yi}}{2}\right)\left(\frac{{v}_{yi}}{g}\right)\phantom{\rule{0ex}{0ex}}{y}_{\mathrm{max}}=\frac{{v}_{yi}^{2}}{2g}$

By knowing the angle of projection , we can find the initial velocity by using the following relation:

Therefore, the initial velocity of the speed is ${v}_{i}=12\text{m}/\text{s}$.

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