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weeeeeb [17]
4 years ago
9

Find the height or length of these natural wonders in km, m, and cm.A. A cave system with a mapped length of 354 miles.B. A wate

rfall that drops 1,235.2 ft.C. A 21320 ft tall mountain.
D. A canyon with a depth of 6630 ft.
Physics
1 answer:
cricket20 [7]4 years ago
4 0

Explanation:

Some standard unit conversion are 1 mile = 1.609344 km, 1 ft.= 30.48 cm,

1 km= 1000 m or 1 m = 0.001 km and 1 m= 100 cm or 1 cm=0.01 m.

Now, use these values to convert the given lengths.

A. length of cave = 5 miles (given)

From standard value 1 mile = 1.609344 km

\Rightarrow 5 miles = \times 1.609344 km= 8.04672 km,

\Rightarrow 5 miles =8.04672 \times 1000 m= 8046.72 m [ as 1 km = 1000 m]

\Rightarrow 5 miles = 8046.72 \times 100 cm=804672 cm

B. Height of the waterfall = 1235 ft. (given)

1 ft.= 30.48 cm [ from standard value]

\Rightarrow 1235.2 ft.= 1235.2\times 30.48 cm=37648.896 cm,

\Rightarrow 1235.2 ft.=37648.896 \times 0.01 m =376.48896 m [ as 1 cm = 0.01 m]

\Rightarrow 1235.2 ft.=376.48896 \times 0.001 km =0.37648896 km [ as 1 m = 0.001 km]

C. Height of the mountain= 21320 ft. (given)

From standard value: 1 ft.= 30.48 cm

\Rightarrow 21320 ft.= 21320 \times 30.48 cm=649833.6 cm,

\Rightarrow 21320 ft.=649833.6 \times 0.01 m =6498.336 m [ as 1 cm = 0.01 m]

\Rightarrow 21320 ft.=6498.336 \times 0.001 km =6.498336 km [ as 1 m = 0.001 km].

D. Depth of canyon =6630 ft.

From standard value: 1 ft.= 30.48 cm

\Rightarrow 6630 ft.= 6630 \times 30.48 cm=202082.4 cm,

\Rightarrow 6630 ft.=202082.4  \times 0.01 m =2020.824  m [ as 1 cm = 0.01 m]

\Rightarrow 6630 ft.=2020.824  \times 0.001 km =2.020824  km [ as 1 m = 0.001 km].

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The focal length will be = 2.67 cm

The distance between the convex lens or a concave mirror and the focal point of a lens or mirror is called the focal length. It is the point where parallel rays of light meet or converge.

given

u (object distance) = 260 cm

v (image distance) = 2.70 cm

f (focal length) = ?

using lens formula

1/f = 1/u + 1/v

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The focal length will be = 2.67 cm

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5 0
2 years ago
The blades of a fan running at low speed turn at 26.2 rad/s. When the fan is switched to high speed, the rotation rate increases
Lady bird [3.3K]

Answer: 1.79\ rad/s^2

Explanation:

Given

Initial angular speed is \omega_1=26.2\ rad/s

Final angular speed is \omega_2=36.5\ rad/s

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Magnitude of the fan's acceleration is given by

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Insert the values

\Rightarrow \alpha=\dfrac{36.5-26.2}{5.75}\\\\\Rightarrow \alpha=\dfrac{10.3}{5.75}\\\\\Rightarrow \alpha=1.79\ rad/s^2

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Scenario 2: Use the following information to answer questions 3 and 4:
NemiM [27]

Answer:

A. 52 min

.A. 47 watts

Explanation:

Given that;

jim weighs 75 kg

and he walks 3.3 mph; the objective here is to determine how long must he walk to expend 300 kcal.

Using the following relation to determine the amount of calories burned per minute while walking; we have:

\dfrac{MET*weight (kg)*3.5}{200}

here;

MET = energy cost of a physical activity for a period of time

Obtaining the data for walking with a speed of 3.3 mph From the  standard chart for MET, At 3.3 mph; we have our desired value to be 4.3

However;

the calories burned in a minute = \dfrac{4.3*75 (kg)*3.5}{200}

= 5.644

Therefore, for walking for 52 mins; Jim  burns approximately 293.475 kcal which is nearest to 300 kcal.

4.

Given that:

mass m = 75 kg

intensity = 6 kcal/min

The eg ergometer work rate = ??

Applying the formula:

V_O_2 ( intensity ) = ( \dfrac{W}{m}*1.8)+7

where ;

V_O_2 ( intensity ) = \dfrac{1 \ kcal min^{-1}*10^{-3}}{5}

V_O_2 ( intensity ) = \dfrac{6*1 \ kcal min^{-1}*10^{-3}}{5}

V_O_2 ( intensity ) = 0.0012

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Since;  6.118kg-m/min is =  1 watt

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4 years ago
A rock is thrown upward from a bridge into a river below. The function f(t)=−16t2+44t+88 determines the height of the rock above
babymother [125]

1) 88 ft

2) 4.09 s

3) 1.38 s

4) 118.2 m

Explanation:

1)

For an object thrown upward and subjected to free fall, the height of the object at any time t is given by the suvat equation:

h(t) = h_0 + ut - \frac{1}{2}gt^2 (1)

where

h_0 is the height at time t = 0

u is the initial vertical velocity

g=32 ft/s^2 is the acceleration due to gravity

The function that describes the height of the rock above the surface at a time t in this problem is

f(t)=-16t^2+44t+88 (2)

By comparing the terms with same degree of eq(1) and eq(2), we observe that

h_0 = 88 ft

which means that the rock is at height h = 88 ft when t = 0: therefore, this means that the height of the bridge above the water is 88 feet.

2)

The rock will hit the water when its height becomes zero, so when

f(t)=0

which means when

0=-16t^2+44t+88

First of all, we can simplify the equation by dividing each term by 4:

0=-4t^2+11t+22

This is a second-order equation, so we solve it using the usual formula and we find:

t_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-11\pm \sqrt{(11)^2-4(-4)(22)}}{2(-4)}=\frac{-11\pm \sqrt{121+352}}{-8}=\frac{-11\pm 21.75}{-8}

Which gives only one positive solution (we neglect the negative solution since it has no physical meaning):

t = 4.09 s

So, the rock hits the water after 4.09 seconds.

3)

Here we want to find how many seconds after being thrown does the rock reach its maximum height above the water.

For an object in free fall motion, the vertical velocity is given by the expression

v=u-gt

where

u is the initial velocity

g is the acceleration due to gravity

t is the time

The object reaches its maximum height when its velocity changes direction, so when the vertical velocity is zero:

v=0

which means

0=u-gt

Here we have

u=+44 ft/s (initial velocity)

g=32 ft/s^2 (acceleration due to gravity)

Solving for t, we find the time at which this occurs:

t=\frac{u}{g}=\frac{44}{32}=1.38 s

4)

The maximum height of the rock can be calculated by evaluating f(t) at the time the rock reaches the maximum height, so when

t = 1.38 s

The expression that gives the height of the rock at time t is

f(t)=-16t^2+44t+88

Substituting t = 1.38 s, we find:

f(1.38)=-16(1.38)^2 + 44(1.38)+88=118.2 m

So, the maximum height reached by the rock during its motion is

h_{max}=118.2 m

Which means 118.2 m above the water.

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