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
WILL GIVE BRAILIEST 70 POINTS First, reflect ABC across the y-axis, then dilate by a factor of ½.
Rina8888 [55]

Answer:

This is the graph one

Step-by-step explanation:

A(-1,-4) -->A' (1,-4)

B(-3,-2) ---> B'(3,-2)

C(-1,2) ---> C(1,2)

5 0
1 year ago
1 Harry Potter but cost $20. To purchase the whole set of seven books it would take 6 times as much. How much would it cost to b
svlad2 [7]

Answer:

$120

Step-by-step explanation:


7 0
3 years ago
Read 2 more answers
The midpoint of AB = ([?],[ ])
3241004551 [841]

Answer:

(0,0)

Step-by-step explanation:

x_{m}=\frac{-2+2}{2}=0\\y_{m}=\frac{-2+2}{2}=0\\

4 0
3 years ago
Given f(x)=3/2x+5 what is f(12)
tigry1 [53]

Answer:

5 and 1/8

Step-by-step explanation:

5 0
3 years ago
Help meh asap<br><br> Write a verbal expression for 4(n + 6)
Sphinxa [80]
Four times the sum of n plus six
3 0
3 years ago
Read 2 more answers
Other questions:
  • Judi solved the equation 1 - 18 = 43. Her work is shown.<br> What error did Judi make?
    8·2 answers
  • In 28% of a sum is $100.80, what is the sum?
    15·2 answers
  • What is the distance between the points (−5, 10) and (−5, 2) ?
    13·2 answers
  • the instantaneous growth rate r of a colony of bacteria t hours after the start of an experiment is given by the function r=0.01
    6·1 answer
  • Ruby uses 1/4 yard of ribbon to make 2 Bows. Which expression shows the length of ribbon in each bow ?
    14·1 answer
  • What is the length of CF? ASAP please!!!
    10·1 answer
  • Car dealers sometimes use the rule of thumb that a car loses about 30% of its value each year. 1. Suppose you bought a new car i
    11·1 answer
  • A cylindrical vase has height 17 in. and radius 3 in. Find the exact surface area of the vase in terms of π. Suppose a second va
    7·1 answer
  • What is 7(m + 4)-2 help me out loooookky
    10·2 answers
  • A manager wants to determine if an employee training program has increased her employees’ customer satisfaction ratings. She ran
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!