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
Vikentia [17]
3 years ago
11

In quadratic drag problem, the deceleration is proportional to the square of velocity

Mathematics
1 answer:
Mars2501 [29]3 years ago
7 0
Part A

Given that a= \frac{dv}{dt} =-kv^2

Then, 

\int dv= -kv^2\int dt \\  \\ \Rightarrow v(t)=-kv^2t+c

For v(0)=v_0, then

v(0)=-kv^2(0)+c=v_0 \\  \\ \Rightarrow c=v_0

Thus, v(t)=-kv(t)^2t+v_0

For v(t)= \frac{1}{2} v_0, we have

\frac{1}{2} v_0=-k\left( \frac{1}{2} v_0\right)^2t+v_0 \\  \\ \Rightarrow \frac{1}{4} kv_0^2t=v_0- \frac{1}{2} v_0= \frac{1}{2} v_0 \\  \\ \Rightarrow kv_0t=2 \\  \\ \Rightarrow t= \frac{2}{kv_0}


Part B

Recall that from part A, 

v(t)= \frac{dx}{dt} =-kv^2t+v_0 \\  \\ \Rightarrow dx=-kv^2tdt+v_0dt \\  \\ \Rightarrow\int dx=-kv^2\int tdt+v_0\int dt+a \\  \\ \Rightarrow x=- \frac{1}{2} kv^2t^2+v_0t+a

Now, at initial position, t = 0 and v=v_0, thus we have

x=a

and when the velocity drops to half its value, v= \frac{1}{2} v_0 and t= \frac{2}{kv_0}

Thus,

x=- \frac{1}{2} k\left( \frac{1}{2} v_0\right)^2\left( \frac{2}{kv_0} \right)^2+v_0\left( \frac{2}{kv_0} \right)+a \\  \\ =- \frac{1}{2k} + \frac{2}{k} +a

Thus, the distance the particle moved from its initial position to when its velocity drops to half its initial value is given by

- \frac{1}{2k} + \frac{2}{k} +a-a \\  \\ = \frac{2}{k} - \frac{1}{2k} = \frac{3}{2k}
You might be interested in
Emilio writes the inequality 17(f+2)+45.99<200 The situation using the variable as to represent the number of friends solve a
larisa [96]

Answer:

7 friends

Step-by-step explanation:

Given the inequality expression

17(g+2)+45.99<200

We are to find the value of g that satisfies the inequality

Expand

17g+34 +45.99<200

17g+79.99<200

Subtract 79.99 from both sides

17g+79.99-79.99<200-79.99

17g<120.01

g<120.01/17

g<7.059

Hence the max number of friend that can attend is 7friends.

7 0
3 years ago
What is the answer to 37+45?
poizon [28]
The answer is 82 because 5+7=12 then 3+4=7 plus the 1 = 82
6 0
3 years ago
Read 2 more answers
How many different arrangements of the letters in the word SCHOOL are there?
pogonyaev
36; there are 6 letters in the word school so if you multiple it by 6 which is the amount of different places one letter could be, the result would be 36
4 0
3 years ago
Read 2 more answers
BRAINIEST AND YOU WILL GET 10 POINTS!
jenyasd209 [6]
1 - The value of p in the equation is p = 0.

2 - The simplified form of the equation is 3x = 1, the reason behind this is when you do the equation, you get x = 1/3. When you do the equation 3x = 1 you get x = 1/3 as well.

3 - The value of z in the equation is z = 13.

4 - In order to figure out what step he did something wrong on, we first need to solve the problem, the answer we will get is x = 2.
To do this the easy way, we can solve each step, and see what one wouldn't equal 2, which the step he did wrong is Step 2.
So, to do Step 2 correctly, it would be: Step 2 - 12x − 6 = 14 + 2x.
6 0
3 years ago
The radius of a cylindrical water tank is 4 ft , and its height is 10 ft . What is the volume of the tank?
Paha777 [63]

Answer:

2010 cu ft to the nearest whole number.

Step-by-step explanation:

Volume = π r^2 h

= 3.14 * 4^3 * 10

= 2009.6

8 0
3 years ago
Other questions:
  • What tupe of group number is 3/4. A. Real, B. Rational, C. Irrational, D. Integer, E. Whole, F. Counting
    11·2 answers
  • Suppose you are organizing a business meeting and are in charge of facilitating the introductions. How would you arrange a group
    10·1 answer
  • Amrita thinks of a number. She doubles it, adds 9 , divides her answer by 3 and finally subtracts 1 . She obtains the same numbe
    5·1 answer
  • Solve for the proportion below. x/24=5/6 <br><br> A. 20 <br> B. 10 <br> C. 12 <br> D. 23
    7·1 answer
  • What is the answer to 2x^3(5x-1)
    14·1 answer
  • What is the slope of the line between (−4, 4) and (−1, −2)? i got -3??????? which isn't an answer.
    9·1 answer
  • A number divided by four is 271. What is the number?
    7·2 answers
  • In a triangle, what is always opposite the angle that has the LEAST measure?
    6·2 answers
  • A dog is leashed to the corner of a house. how much running area does the dog have? 40 ft
    15·1 answer
  • The October 31 bank statement of the Stover Co. indicated a balance of $6,151.11. Stover’s checkbook reflected a balance of $2,1
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!