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kompoz [17]
3 years ago
5

A boat can travel 1010 miles against a current in the same time that it can travel 110110 miles with the current. The rate of th

e current is 55 mph. Find the rate of the boat in still water.
Physics
1 answer:
Marizza181 [45]3 years ago
3 0

Answer:

56.02 mph

Explanation:

Let the velocity of boat in still water is, v

Given that velocity of the current is 55 mph

Now, velocity against current is, v-55

velocity along the current is v+55.

And according to question, time taken by boat to travel 1010 miles against the current is equivalent to time take to travel 110110 miles with the current.

Therefore,

Time taken against the current is, t=\frac{1010}{v-55}

Time taken with the current is, t=\frac{110110}{v+55}

Now this time is equal.

Therefore,

\frac{1010}{v-55}=\frac{110110}{v+55}\\\frac{{v+55}}{{v-55}} =109.02\\v+55=109.02(v-55)\\v=56.02mph

Therefore, this is the velocity in still water.

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The central star of a planetary nebula emits ultraviolet light with wavelength 104nm. This light passes through a diffraction gr
Gala2k [10]

Answer: 31.33 degrees

Explanation:

The diffraction angles \theta_{n} when we have a slit divided into n parts are obtained by  the following equation:

dsin\theta_{n}=n\lambda   (1)

Where:

d is the width of the slit

\lambda  is the wavelength of the light

n is an integer different from zero.

Now, the first-order diffraction angle is given when n=1, hence equation (1) becomes:

dsin\theta_{1}=\lambda   (2)

Now we have to find the value of \theta_{1}:

sin\theta_{1}=\frac{\lambda}{d}  

\theta_{1}=arcsin(\frac{\lambda}{d})   (3)

We know:

\lambda=104nm=104(10)^{-9}m

In addition we are told the diffraction grating has 5000 slits per mm, this means:

d=\frac{1mm}{5000}=\frac{1(10)^{-3}m}{5000}

Substituting the known values in (3):

\theta_{1}=arcsin(\frac{104(10)^{-9}m}{\frac{1(10)^{-3}m}{5000}})

\theta_{1}=arcsin(0.52)

<u>Finally:</u>

\theta_{1}=31.33\º >>>This is the first-order diffraction angle

4 0
3 years ago
The current in some DC circuits decays according to the function I=I0e−t/τ, where I is the current at some point in time, I0 is
almond37 [142]

Answer: 1.95

Explanation:

You should start off from the decay formula and solve for τ:

I = I_{0}e^{\frac{t}{\tau\\  } }

\frac{I}{I_{0}} = e^{\frac{-t}{\tau} }

Apply inverse logarithmic function:

ln(\frac{0.2 A}{1.2 A} ) = \frac{-t}{\tau}

The final form will be:

\tau=\frac{-3.5s}{ln(\frac{0.2A}{1.2A} )}

Inputing values for I, IO, and t:

\tau=\frac{-3.5S}{ln(\frac{0.2 A}{1.2 A} )} = 1.95

3 0
3 years ago
Drag the tiles to the correct boxes to complete the pairs.
Dimas [21]
Brown dwarf is the first box
White dwarf is the second box
Black dwarf is the third box
Red giant is the fourth box
And
Black hole is the last box
5 0
2 years ago
Select the correct location on the image.
slega [8]

Answer:

orange line

Explanation:

it is the only straight line that makes sense. curved lines imply velocity changed. and the completly flat green line implies the vehicle didn't move since its position value stayed the same. must be the downward pointing orange line

8 0
2 years ago
Who was nikola teslas partner​
vesna_86 [32]

Answer:

Thomas Edison

Explanation:

6 0
3 years ago
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