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
Jane has 6/7 of a yard of ribbon. She uses 3/4 of a yard to trim an ornament. how much ribbon is left?
Degger [83]

Answer:

2/28

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
1.) y + 3 > 7 what’s the answer?
sasho [114]

Answer:

Yes you are right it is option 4

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
PLEASE HELP ASAP
zheka24 [161]

Answer:

the second forth and fifth on the graph.

Step-by-step explanation: have a good day!

5 0
2 years ago
A triangle has an area of 80 yards and a height of 10 yards how long is the base of the triangle
Wewaii [24]
16 yards is your answer for this!
its 2 with area/hight. 
if you need the steps of this just ask ill show you how to do it step by step
5 0
3 years ago
Determine all the unknown values of the figure below.
Vanyuwa [196]

Answer:

F=10, S=26

Step-by-step explanation:

We know that the base is 24. Using that information, 10^2+24^2=26^2 which is a pythagorean triple

3 0
3 years ago
Other questions:
  • Solve the inequality-2(6+s)_>-15-2s
    11·2 answers
  • Levi wants to order the fractions 1/3, 2/5, and 11/30 in descending order? How can you help him by using a common denominator? E
    14·1 answer
  • What is the value of the digit 6 in 968,743,220 ?
    8·1 answer
  • If you spin the spinner 50 times, how many times do you expect it to land on 10?
    7·2 answers
  • An express plane is travelling at 50 km/h. How far does it go in 1 day?.​
    11·1 answer
  • Who tryna okay among us??
    9·2 answers
  • Can someone solve this please!
    12·2 answers
  • The equation 2x^2+5kx+k=0, where k is a constant has no real roots. Find possible values of k
    12·1 answer
  • Help my math please<br>please ​
    11·2 answers
  • This pattern can be<br> represented by the explicit<br> expression of 2n.
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!