Linear expansivity?

The surface of the dock is 6 feet above the water. If you pull the rope in at a rate of 2 ft/sec, how quickly is the boat approa

Oduvanchick [21]

Answer:

The boat is approaching the dock at a rate of 2.5 ft/s.

Explanation:

Let the rope length be 'l' at any time 't', the distance of boat from dock be 'b' at any time 't'.

Given:

The height of dock above water (h) = 6 feet

Rate of pull of rope or rate of change of rope is, $\frac{dl}{dt}=2\ ft/s$

As clear from the question, the height is fixed and only the length 'l' and distance 'b' varies with time 't'.

Now, the above situation represents a right angled triangle as shown below.

Using Pythagoras Theorem, we have:

$l^2=h^2+b^2\\\\l^2=6^2+b^2\\\\l^2=36+b^2----------(1)$

Now, differentiating the above equation with time 't', we get:

$2l\frac{dl}{dt}=0+2b\frac{db}{dt}\\\\l\frac{dl}{dt}=b\frac{db}{dt}\\\\\frac{db}{dt}=\frac{l}{b}\frac{dl}{dt}------(2)$

Now, the distance 'b' can be calculated using 'l=10 ft' in equation (1). This gives,

$b^2=10^2-36\\\\b=\sqrt{64}=8\ ft$

Now, substituting all the given values in equation (2) and solve for $\frac{db}{dt}$ . This gives,

$\frac{db}{dt}=\frac{10}{8}\times 2\\\\\frac{db}{dt}=2.5\ ft/s$

Therefore, the boat is approaching the dock at a rate of 2.5 ft/s.

7 0

2 years ago

The maximum gauge pressure in a hydraulic lift is 18.0 atm what is the largest size vehicle

victus00 [196]

There is a missing part in the question. Found the complete text on internet:
"What is the largest size vehicle (kg) it can lift if the diameter of the output line is 28.0 cm? "

Solution
The diameter of the piston is 28.0 cm, this means its radius is 14.0 cm (half the diameter), so the area of the piston is
 $A=\pi r^2 = \pi (0.14 m)^2 =6.15 \cdot 10^{-2} m^2$

The maximum pressure of the lift is
 $p=18.0 atm = 1.82 \cdot 10^6 Pa$

Therefore the maximum force the piston can lift is
 $F=pA=(1.82 \cdot 10^6 Pa)(6.15 \cdot 10^{-2} m^2)=1.12 \cdot 10^5 N$

And the size (the mass) of the vehicle is
 $m= \frac{F}{g}= \frac{1.12 \cdot 10^5 Pa}{9.81 m/s^2} =1.14 \cdot 10^4 kg$

3 0

3 years ago

A 2.0 kg wood block is launched up a wooden ramp that is inclined at a 30° angle. The block’s initial speed is 10 m/s. What vert

Romashka [77]

Answer:

Vertical Height = 0.784 meter, Speed back at starting point = 10 m/s

Explanation:

Given Data:

V is the overall velocity vector, $Vi$ and $Ui$ are its initial vertical and horizontal components

$R = 10 m/s\\ Projection Angle (theta) = 30 degrees\\Vi = 10*sin(30) = 5 m/s\\Ui = 10*cos(30) = 8.66 m/s$

To find:

Max Height $h$ achieved

Calculation:

1) Using the $3^{rd}$ equation of motion, we know

$2*a*s = Vf^{2} - Vi^{2}$

2) In terms of gravity $g$ height $h$ and the vertical component of Velocity $Vf , Vi$ .

3) As $Vf = 0$ as at maximum height the vertical component of velocity is zero maximum height achieved

$2*g*h = Vf^{2} -Vi^{2}$

putting values

4) $h = 0.784 m/s$

5) As for the speed when it reaches back its starting point, it will have a speed similar to its launching speed, the reason being the absence of air friction (Air drag)

3 0

3 years ago

1. Given an element's atomic number and mass number, how can you tell the number of protons and neutrons in its nucleus?

DanielleElmas [232]

C. Number of protons = atomic number; number of neutrons = mass number - atomic number

8 0

2 years ago

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A teacher wants to perform a classroom demonstration that illustrates both chemical and physical changes. Which would be the bes

anygoal [31]

Answer

D) burning a candle

Explanation

When burning a candle no new substance is form.

We have both physical and chemical change occuring.

Physical part: Melting of the solid wax and evaporation of the liquid forms the physical change.

Chemical part: burning of the wax vapour forms the chemical change.

7 0

2 years ago

Read 2 more answers

Linear expansivity?​

Linear expansivity?