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3 years ago

12

An Olympic runner leaps over a hurdle. The acceleration of gravity is 9.81 m/s2 . If the runner’s initial vertical speed is 2.0

m/s, how much will the runner’s center of mass be raised during the jump?

1 answer:

alisha [4.7K]3 years ago

3 0

Consider the upward direction of motion as positive and downward direction of motion as negative.

a = acceleration due to gravity in downward direction = - 9.81 $\frac{m}{s^{2}}$

v₀ = initial velocity of runner in upward direction = 2.0 $\frac{m}{s}$

v = final velocity of runner at the highest point = 0 $\frac{m}{s}$

x = distance by which center of mass of runner rise = ?

Using the kinematics

v² = v²₀ + 2 a x

inserting the values

0² = 2² + 2 (- 9.81) x

x = 0.204 m

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The flow rate over Niagara falls is 84,760 cfs (cubic feet per second), and the drop from top to bottom is 167 feet. If this flo

jekas [21]

To develop this problem we will calculate the volume from the given flow (volume per unit of time). This process will be accompanied by transforming the units given in the International system.

Through the density-volume-mass ratio, we will calculate the mass. Finally we will proceed to calculate the total power generated.

1 feet = 0.3048 m

$\dot{V} = 84760ft^3/s$

$\dot{V} = 84760ft^3/s (\frac{(0.3058m)^3}{(1ft)^3})$

$\dot{V} = 2400m^3/s \text{and the Volume each second is } V= 2400m^3$

Now the mass of water falling down each second would be

$\rho = \frac{m}{V} \rightarrow m = \rho V$

$m = (1000kg/m^3)(2400m^3)$

$m = 2.4*10^6kg$

Now Height in meters is

$h = 167 ft (\frac{(0.3058m)}{(1ft)})$

$h= 50.9 m$

The power produced is equivalent to the work done by gravity over a certain time. At this case that can be expressed as,

$P = \frac{W}{t}\\P = \frac{F*h}{t}\\P = \frac{mgh}{t}\\P = \frac{2.4*10^6*9.8*50.9}{1}\\P = 1.197*10^9 Watts$

The power of Niagara Falls then would be 1.197GW while the power generated by the Three Gorges Dam is 22,500 MW. This indicates that the Niagara Falls, if it were a dam that covered 100% of the fluid it carries, would exceed the production of the dam in China by thousands.

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4 years ago

The mass of a sample of sodium bicarbonate is 2. 1 kilograms (kg). There are 1,000 grams (g) in 1 kg, and 1 Times. 109 nanograms

slega [8]

2.1 kg of sodium bicarbonate is equal to the 2.1 x 10¹² ng of sample. Option D is correct.

Mass is the quantity of the substance in the body or object. The SI unit of mass is Kilogram.

There are other units of measure,

Milligram: 1 g is equal to the $\bold {10^3 \ mg}$

Micro-gram: 1 g is equal to $\bold {10^{6} \ \mu g}$

Nano-gram: 1 g is is equal to $\bold {10^{9} \ ng}$

First convert kg to gram,

Since, 1 Kg = 1000 g

2.1 kg = grams of sample

So,

Do the cross multiplication,

$\rm mass\ of\ sample = \dfrac {2.1\ kg \times 1000\ g }{ 1 kg}\\\\\rm mass\ of\ sample =2100 g$

Now, convert 2100 g to nano-grams

Since, 1 g = 1 x 10⁹ ng

2100 g = ng of sample

So,

Do the cross multiplication,

$\rm mass\ of\ sample = \dfrac {2100 g \times 1 \times 10^9 ng }{1\ g}\\\\\rm mass\ of\ sample = 2.1 \times 10^1^2 ng$

Therefore, 2.1 kg of sodium bicarbonate is equal to the 2.1 x 10¹² ng of sample.

To know more about Mass units,

brainly.com/question/489186

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3 years ago

Determine the speed, wavelength, and frequency of light from a helium-neon laser as it travels through polystyrene. The waveleng

klemol [59]

Answer:

Speed:

$2.01x10^{8}m/s$

Wavelength:

$4.24x10^{-7}m$

Frequency:

$4.74x10^{14}Hz$

Explanation:

The speed of the laser as it travels through polystyrene can be determine by means of the equation of the refraction index:

$n = \frac{c}{v}$ (1)

Where c is the speed of light and v is the speed of the laser in the medium.

Therefore, v will be isolated from equation 1

$v = \frac{c}{n}$

$v = \frac{3x10^{8}m/s}{1.490}$

$v = 2.01x10^{8}m/s$

Hence, the speed of the laser has a value of $2.01x10^{8}m/s$

Frenquency:

Since, wavelength is the only one who depends on the media. Therefore the frequency in both medium will be the same.

To determine the frequency it can be used the following equation

$c = \nu \cdot \lambda$ (2)

Where c is the speed of light, $\nu$ is the frequency and $\lambda$ is the wavelength

Then, $\nu$ wil be isolated from equation 2.

$\nu = \frac{c}{\lambda}$ (3)

Before using equation 3 it is necessary to express $\lamba$ in units of meters.

$\lambda = 632.8nm . \frac{1m}{1x10^{9}nm}$ ⇒ $6.328x10^{-7}m$

$\nu = \frac{3x10^{8}m/s}{6.328x10^{-7}m}$

$\nu = 4.74x10^{14}s^{-1}$

$\nu = 4.74x10^{14}Hz$

Hence, the frequency of the laser has a value of $4.74x10^{14}Hz$

Wavelength:

To determine the wavelength it can be used:

$v = \nu \cdot \lambda$

$\lambda = \frac{v}{\nu}$

Where v is the speed of the laser through the polystyrene.

$\lambda = \frac{2.01x10^{8}m/s}{4.74x10^{14}s^{-1}}$

$\lambda = 4.24x10^{-7}m$

Hence, the wavelength of the laser has a value of $4.24x10^{-7}m$

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4 years ago

A girl has a weight of 450 N and her feet have a total area of 0.0300 m2. Calculate the pressure her feet put on the ground.

GenaCL600 [577]

Answer:

15000N/m²

Explanation:

Given parameters:

Weight = 450N

Total area = 0.03m²

Unknown:

Pressure under her feet = ?

Solution:

Pressure is the force per unit area on a body.

Pressure = $\frac{Force }{Area}$

Weight is a type of force;

Pressure = $\frac{450}{0.03}$ = 15000N/m²

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4 years ago