1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kherson [118]
3 years ago
11

When the velocity v of an object is very​ large, the magnitude of the force due to air resistance is proportional to v squared w

ith the force acting in opposition to the motion of the object. A shell of mass 2 kg is shot upward from the ground with an initial velocity of 600 ​m/sec. If the magnitude of the force due to air resistance is ​(0.1​)v squared​, when will the shell reach its maximum height above the​ ground? What is the maximum​ height? Assume the acceleration due to gravity to be 9.81 m divided by s squared.
Mathematics
1 answer:
Sati [7]3 years ago
4 0

Answer:

Step-by-step explanation:

The model fo the shell is given by the following equation of equilibrium:

\Sigma F = -b\cdot v^{2} - m\cdot g = m\cdot \frac{dv}{dt}

This first-order differential equation has separable variables, which are cleared herein:

\int\limits^t_{0\,s} \, dt = -\frac{m}{b} \int\limits^{0\,\frac{m}{s} }_{600\,\frac{m}{s} } {\frac{1}{ v^{2}+\frac{m}{b}\cdot g } } \, dv

The solution of this integral is:

t = -\frac{m}{2b}\cdot \left[\tan^{-1} \left(\frac{v}{\sqrt{\frac{m\cdot g}{b} } }\right) - \tan^{-1} \left(\frac{600}{\sqrt{\frac{m\cdot g}{b} } }\right)\right]

\tan^{-1} \left(\frac{v}{\sqrt{\frac{m\cdot g}{b} } }  \right)=-\frac{2\cdot b\cdot t}{m} + \tan^{-1}\left(\frac{600}{\sqrt{\frac{m\cdot g}{b} } }  \right)

\frac{v}{\sqrt{\frac{m\cdot g}{b} } }=\tan \left[-\frac{2\cdot b\cdot t}{m} + \tan^{-1}\left(\frac{600}{\sqrt{\frac{m\cdot g}{b} } }  \right)\right]

v = \sqrt{\frac{m\cdot g}{b} } \left [\frac{\tan \left(-\frac{2\cdot b \cdot t}{m}  \right)+ \left(\frac{600}{\sqrt{\frac{m\cdot g}{b} } }  \right)}{1 - \left(\frac{600}{\sqrt{\frac{m\cdot g}{b} } }  \right)\cdot \tan \left(-\frac{2\cdot b \cdot t}{m}  \right) }\right]

You might be interested in
Mark and his 3 friends agreed to join the School’s talent show. They then decided how to pick the song that they will sing for t
laiz [17]

Answer:

  • 1/6

Step-by-step explanation:

In order to get to choose the song Mark needs to roll a 1 since a 2 is the smallest number already rolled.

<u>Probability of rolling a 1 is:</u>

  • P(1) = 1/6
8 0
3 years ago
Which equivalent fractions can you use to find the sum of 2/8 + 3/9?
sattari [20]
You can you 72 which would make 2/8 18/72 and 3/9 24/72 which makes the sum 42/72.
7 0
3 years ago
5 and 1/4 divided by negative 6 simplify
Zanzabum

Answer:

-0.875

Step-by-step explanation:

5 1/4 = 5.25

5.25/ -6 = -0.875

8 0
2 years ago
Read 2 more answers
Suppose a railroad rail is 3 kilometers and it expands on a hot day by 15 centimeters in length. Approximately how many meters w
earnstyle [38]

Answer:

Answer:  13.4 m

Step-by-step explanation:

For small angles, x, in radians,

tan(x) ≈ sin(x) = x

Use this to create an approximate diagram for the problem as shown in the figure below.

The actual deflected shape is parabolic, but it is approximated by an isosceles triangle with small equal angles.

The extend length is 3 km + 12 cm, which is 

3000 + 0.12 = 3000.12 m

Half of the extended length is 1500.06 m

Let h+  the rise of the center of the rail above ground.

From the Pythagorean theorem, obtain

h² + 1500² = 1500.6²

h² = 1500.06² - 1500² = 180.004

h = 13.4 m, which is about 0.9% of the original length.

Read more on Brainly.com - brainly.com/question/5596356#readmore

6 0
2 years ago
How do you factor this polynomial expression?
alexdok [17]
9{ x }^{ 2 }-25\\ \\ ={ 3 }^{ 2 }{ x }^{ 2 }-{ 5 }^{ 2 }\\ \\ ={ \left( 3x \right)  }^{ 2 }-{ 5 }^{ 2 }\\ \\ =\left( 3x+5 \right) \left( 3x-5 \right)
3 0
3 years ago
Read 2 more answers
Other questions:
  • What's an area model
    12·1 answer
  • mary made 15 000 ml of lemonade FOR HER PARTY, AND SHE SERVED THE LEMONADE DIVIDED EQUALLY INTO 8 PITCHERS. HER FRIEND DRANK 6 P
    6·1 answer
  • Scarlett is playing a video game she spends 900 minerals to create 18 workers each worker costs the same number of minerals writ
    6·2 answers
  • A rectangle has a width of 40 units and a length of 52 units. What is the length of the diagonals of the rectangle
    13·2 answers
  • Dan rolled a number cube 20 times. the cube landed on fhe number 3 six times.
    6·1 answer
  • Who is correct and why?
    12·1 answer
  • What is 7.7 tons roundef to the nearest ton
    15·2 answers
  • Identify the center and radius of each. Photo attached.
    11·1 answer
  • Help me plsssssssssssssssss​
    5·1 answer
  • Quadrilateral PQRS is transformed to create quadrilateral P’Q’R’S
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!