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3 years ago

6

Stacy travels 5 times as fast as Eric. Traveling in opposite directions, they are 336 miles apart after 4 hours. Find their rate

s of travel.

1 answer:

Vilka [71]3 years ago

6 0

Answer:

Eric travelled at 21miles per hour

while stacy travelled at 105miles per hour.

Explanation:

speed = distance/time

then distance = speedxtime.

speed = x

time = 4hrs

Eric's distance after 4hrs = 4x

since stacy is 5 times faster than eric =

stacy's distance = (5x)4 = 20x

Stacy's distance - Eric's distance = 336m

20x - 4x = 336Miles

16x = 336miles

x = 336/16

x = 21miles per hour

so Eric was travelling at 21miles per hour

While Stacy was travelling at 105 miles per hour.

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(a) 3.58 km 45° south of east

The total displacement is given by:

$d=vt$

where

v is the average velocity

t is the time

The average velocity is:

v = 3.53 m/s

While we need to convert the time from minutes to seconds:

$t=169 min \cdot 60 s/min = 10140 s$

Therefore, the magnitude of the displacement is

$d=(3.53)(10140)=35794 m = 3.58 km$

And the direction is the same as the velocity, therefore 45° south of east.

(b) 5.53 m/s 90° south of east

The velocity of the air relative to the ground is

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and the direction is exactly opposite to that of Allen, so it is 45° north of west. Allen's velocity relative to the ground is

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So this must be the resultant of Allen's velocity relative to the air (v') and the air's speed ( $v_a$ ). Since these two vectors are in opposite direction, we have

$v= v'-v_a$

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$v'=v+v_a = 3.53 + 2.00 = 5.53 m/s$

The direction must be measured relative to the air's reference frame. In this reference frame, Allen is moving exactly backward, so his direction will be 90° south of east.

(c) 56.1 km at 90° south of east.

Since Allen's velocity relative to the air is

v' = 5.53 m/s

Then the displacement of Allen relative to the air will be given by

$d'=v't$

and substituting,

$d'=(5.53)(10140)=56074 m = 56.1 km$

And the direction is the same as that of the velocity, therefore will be 90° south of east.

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4 years ago

An aluminum cylinder with a radius of 2.7 cm and a height of 67 cm is used as one leg of a workbench. The workbench pushes down

soldier1979 [14.2K]

Answer:

$1.9\times 10^{-4}$

$1.2\times 10^{-4}\ m$

Explanation:

r = Radius = 2.7 cm

F = Force = $3.2\times 10^4\ N$

A = Area = $\pi r^2$

$\sigma$ = Stress = $\frac{F}{A}$

E = Young's modulus = $7\times 10^{10}\ Pa$

$\epsilon$ = Strain

$L_0$ = Original length = 67 cm

$\Delta L$ = Change in length

Young's modulus is given by

$E=\frac{\sigma}{\epsilon}\\\Rightarrow \epsilon=\frac{\sigma}{E}\\\Rightarrow \epsilon=\frac{\frac{3.2\times 10^4}{\pi 0.027^2}}{7\times 10^{10}}\\\Rightarrow \epsilon=0.0001996=1.9\times 10^{-4}$

Strain is $1.9\times 10^{-4}$

Strain is given by

$\epsilon=\frac{\Delta L}{L_0}\\\Rightarrow \Delta L=\epsilon\times L_0\\\Rightarrow \Delta L=1.9\times 10^{-4}\times 0.67\\\Rightarrow \Delta L=0.0001273\\\Rightarrow \Delta L=1.2\times 10^{-4}\ m$

The cylinder height decreases by $1.2\times 10^{-4}\ m$

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If we analyze an atom within the molecule, its last shell is full, in the case of atoms with few electrons in this shell, they are lost and in the case of many electors in this shell, it gains electrons to have eight (8) in total.

When reviewing the different answers, the correct one is:

* The third shell would be empty, so the eight electrons on the second level would be the outermost after the atom lost one electron

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