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Rainbow [258]
3 years ago
6

A severe storm on January 10, 1992, caused a cargo ship near the Aleutian Islands to spill 29,000 rubber ducks and other bath to

ys into the ocean. Ten months later hundreds of rubber ducks began to appear along the shoreline near Sitka, Alaska, roughly 1600 miles away.
What was the approximate average speed of the ocean current that carried the ducks to shore in m/s and in mi/h? (Rubber ducks from the same spill began to appear on the coast of Maine in July 2003.)
Physics
1 answer:
Anna35 [415]3 years ago
6 0
The distance that the rubber ducks traveled = 1600 miles.
The time taken to travel this distance = 10 months.

By definition, the approximate average speed of the ocean is
v = (1600 miles)/(10 months)

Note that
1 mile = 1609 m 
10 months = (10 months)*(30 days/month) *(24 hours/day)
                  = 7200 hours (approx.)
                  = 7200*3600 = 2.592 x 10⁷ s

Therefore
v = \frac{(1600 \, m)*(1609 \, \frac{m}{mi}) }{(10 \, months)*(2.592 \times 10^{7} \, \frac{s}{10 \, months}) } = 0.0993 \, \frac{m}{s}

Also,
v = \frac{1600 \, m}{7200 \, h} =0.222 \, \frac{mi}{h}

Answer:
The average velocity is approximately 0.1 m/s, or 0.222 m/h. 

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series RC circuit is built with a 15 kΩ resistor and a parallel-plate capacitor with 18-cm-diameter electrodes. A 18 V, 36 kHz s
andre [41]

Answer:

d=1.84\ mm

Explanation:

<u>Capacitance</u>

A two parallel-plate capacitor has a capacitance of

\displaystyle C=\frac{\epsilon_o A}{d}

where

\epsilon_o=8.85\cdot 10^{-12}\ F/m

A = area of the plates = \pi r^2

d = separation of the plates

\displaystyle d=\frac{\epsilon_o A}{C}=\frac{\epsilon_o \pi r^2}{C}

We need to compute C. We'll use the circuit parameters for that. The reactance of a capacitor is given by

\displaystyle X_c=\frac{1}{wC}

where w is the angular frequency

w=2\pi f=2\pi \cdot 36000=226194.67\ rad/s

Solving for C

\displaystyle C=\frac{1}{wX_c}

The reactance can be found knowing the total impedance of the circuit:

Z^2=R^2+X_c^2

Where R is the resistance, R=15 K\Omega=15000\Omega. Solving for Xc

X_c^2=Z^2-R^2

The magnitude of the impedance is computed as the ratio of the rms voltage and rms current

\displaystyle Z=\frac{V}{I}

The rms current is the peak current Ip divided by \sqrt{2}, thus

\displaystyle Z=\frac{\sqrt{2}V}{I_p}

I_p=0.65\ mA/1000=0.00065\ A

Now collect formulas

\displaystyle X_c^2=Z^2-R^2=\left(\frac{\sqrt{2}V}{I_p}\right)^2-R^2

Or, equivalently

\displaystyle X_c=\sqrt{\frac{2V^2}{I_p^2}-R^2}

\displaystyle X_c=\sqrt{\frac{2\cdot 18^2}{0.00065^2}-15000^2}

X_c=36176.34\ \Omega

The capacitance is now

\displaystyle C=\frac{1}{226194.67\cdot 36176.34}=1.22\cdot 10^{-10}\ F

The radius of the plates is

r=18\ cm/2=9 \ cm = 0.09 \ m

The separation between the plates is

\displaystyle d=\frac{8.85\cdot 10^{-12} \cdot \pi\cdot 0.09^2}{1.22\cdot 10^{-10}}

d=0.00184\ m

\boxed{d=1.84\ mm}

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