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3 years ago

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Calculate the Reynolds number for a person swimming through maple syrup. The density of syrup is about 1400 kg/m^3 and the visco

sity is about 0.5 Pa's. A person is about 2m in length and can swim about 1 m/s.

1 answer:

Tema [17]3 years ago

5 0

Answer:

The Reynolds number is 5600.

Explanation:

Given that,

Density = 1400 kg/m³

Viscosity = 0.5 Pa's

Length = 2 m

Speed = 1 m/s

We need to calculate the Reynolds number

Using formula of Reynolds number

$R_{e}=\dfrac{\rho V\times L}{\mu}$

Where, $\rho$ = density of fluid

v = speed of syrup

l = length of a person

$\mu$ =Viscosity

Put the all value into the formula

$R_{e}=\dfrac{1400\times1\times2}{0.5}$

$R_{e}=5600$

Hence, The Reynolds number is 5600.

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You are standing in a building whose height (40m) you throw a ball downward at a angle of -30 at a speed of (10m/s) acceleration

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Explanation:

Assuming the question is to find the time $t$ the ball is in air, we can use the following equation:

$y=y_{o}+V_{o}sin \theta t-\frac{1}{2}gt^{2}$

Where:

$y=0m$ is the final height of the ball

$y_{o}=40 m$ is the initial height of the ball

$V_{o}=10 m/s$ is the initial velocity of the ball

$t$ is the time the ball is in air

$g=9.8 m/s^{2}$ is the acceleration due to gravity

$\theta=30\°$

Then:

$0 m=40 m+(10 m/s)(sin(30\°))t-\frac{1}{2}9.8 m/s^{2}t^{2}$

$0 m=40 m+5m/s t-4.9 m/s^{2}t^{2}$

Multiplying both sides of the equation by -1 and rearranging:

$4.9 m/s^{2}t^{2}-5m/s t-40 m=0$

At this point we have a quadratic equation of the form $at^{2}+bt+c=0$ , which can be solved with the following formula:

$t=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$

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$a=4.9$

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Substituting the known values:

$t=\frac{-(-5) \pm \sqrt{(-5)^{2}-4(4.9)(-40)}}{2(4.9)}$

Solving the equation and choosing the positive result we have:

$t=3.41 s$ This is the time the ball is in air

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