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
joja [24]
3 years ago
12

The rate of change of the downward velocity of a falling object is the acceleration of gravity (10 meters/sec 2) minus the accel

eration due to air resistance. Suppose that the acceleration due to air resistance is 0.1 inverse seconds times the downward velocity. Write the initial value problem and the solution for the downward velocity for an object that is dropped (not thrown) from a great height. dv -10-0.1v y(t)-| 10-10e-0.1 x what is the terminal velocity?meters/second How long before the object reaches 90% of terminal velocity? How far has it fallen by that time? seconds ,namwww.janv. Progr?? .Practoe Another venion
Mathematics
1 answer:
Alexus [3.1K]3 years ago
3 0

Answer:

See below

Step-by-step explanation:

Write the initial value problem and the solution for the downward velocity for an object that is dropped (not thrown) from a great height.

if v(t) is the speed at time t after being dropped, v'(t) is the acceleration at time t, so the the initial value problem for the downward velocity is

v'(t) = 10 - 0.1v(t)

v(0) = 0 (since the object is dropped)

<em> The equation v'(t)+0.1v(t)=10 is an ordinary first order differential equation with an integrating factor </em>

\bf e^{\int {0.1dt}}=e^{0.1t}

so its general solution is  

\bf v(t)=Ce^{-0.1t}+100

To find C, we use the initial value v(0)=0, so C=-100

and the solution of the initial value problem is

\bf \boxed{v(t)=-100e^{-0.1t}+100}

what is the terminal velocity?

The terminal velocity is

\bf \lim_{t \to\infty}(-100e^{-0.1t}+100)=100\;mt/sec

How long before the object reaches 90% of terminal velocity?

90%  of terminal velocity = 90 m/sec

we look for a t such that

\bf -100e^{-0.1t}+100=90\rightarrow -100e^{-0.1t}=-10\rightarrow e^{-0.1t}=0.1\\-0.1t=ln(0.1)\rightarrow t=\frac{ln(0.1)}{-0.1}=23.026\;sec

How far has it fallen by that time?

The distance traveled after t seconds is given by

\bf \int_{0}^{t}v(t)dt

So, the distance traveled after 23.026 seconds is

\bf \int_{0}^{23.026}(-100e^{-0.1t}+100)dt=-100\int_{0}^{23.026}e^{-0.1t}dt+100\int_{0}^{23.026}dt=\\-100(-e^{-0.1*23.026}/0.1+1/0.1)+100*23.026=1,402.6\;mt

You might be interested in
PLEASE HEEEEEEEEEEEEEEEEEELP
inna [77]
I’m pretty sure it’s 3 and a 2
8 0
3 years ago
Mr. Brown shares with the class that 70% of the students got an A on the English vocabulary quiz. If Mr. Brown has 100 students,
mezya [45]

Answer:

a. \frac{70}{100}

b. 0.7

c. 0.7=70%=\frac{70}{100}

Step-by-step explanation:

70% of 100 received an A, that is 70/100 times 100 equal to 70

\frac{70}{100}*100=70

a. 70% = \frac{70}{100}

b. \frac{70}{100} = 0.7

Notice that 70/100 is equal to 7/10 which is 0.7

c. 0.7=70%=\frac{70}{100}  

5 0
3 years ago
If Dora was born in 1981 and her son was born 25 years after that what is an equation that could help solve that
Gnom [1K]
1981+25
Since she was born in the year 1981, and her son was born 25 years later so you add 25
4 0
3 years ago
Read 2 more answers
Find the volume (Don't forget your UNITS) *
Radda [10]

Answer:

135 cm³

Step-by-step explanation:

  1. To find volume: you multiply length*width*height

    2. l*w*h

    3. 6*5*4 1/2

    4. 6*5=30

    5. 30*4 1/2=135

    6. 135 cm³

Hope this helped!! :)

Stay safe and have a wonderful day/night!!!!!

Brainliest?!?!

5 0
2 years ago
When you multiply any whole number by the one before it, the result is always an even number.
polet [3.4K]
Verrrrrrry interesting ! / / / Every multiple of an even number is another even number. When you take any whole number and the one 'before' it ... no matter which direction 'before' means .... one of the numbers is even. So their product is a multiple of an even number, and it must be another even number.
8 0
3 years ago
Other questions:
  • Bacteria live in groups called colonies colonies are usually circular the diameter distance across if a particular bacterial col
    9·1 answer
  • Marc bought a giant submarine sandwich for his party. The sandwich was cut into 6 pieces. Each piece was 1/2 foot long.
    10·2 answers
  • At a supermarket in France, the price of apples is 2.50 euros per kilogram. Suppose the exchange rate is 1 euro =$1.34. Whoa is
    11·1 answer
  • Find the inverse function of <img src="https://tex.z-dn.net/?f=y%3D3%5E%7Bx-2%7D" id="TexFormula1" title="y=3^{x-2}" alt="y=3^{x
    8·1 answer
  • To determine student's final grade for a math class, Mr. Abbot throws out the lowest test score and takes the average of the rem
    9·1 answer
  • Solve for x in the equation.
    11·1 answer
  • ?????????????????????????
    9·1 answer
  • Internet prices for glasses are often considerably lower than those at the brick and mortar stores but quality is another questi
    15·1 answer
  • Write an equation of the line that passes through each pair of points.
    7·1 answer
  • Find unknown angles, value of 'x' and unknown sides:​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!