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
ipn [44]
3 years ago
14

"Suppose an object falling in the atmosphere has mass m=15kg and the drag coefficient is γ=9kg/s. Recall that the differential e

quation governing the motion of the particle is given by mv′=mg−γv(∗).If the velocity of the object at time t=0s is v(0)=9.55m/s, find the solution of the differential equation given in (∗) corresponding to this initial value (use g=9.8 and do not worry about units),Answer: v(t)= ?find the velocity of the object at time t=0.5s (be sure to enter units). Answer: ?"
Mathematics
1 answer:
Art [367]3 years ago
6 0

Answer:

a. v(t)= -6.78e^{-16.33t} + 16.33 b. 16.33 m/s

Step-by-step explanation:

The differential equation for the motion is given by mv' = mg - γv. We re-write as mv' + γv = mg ⇒ v' + γv/m = g. ⇒ v' + kv = g. where k = γ/m.Since this is a linear first order differential equation, We find the integrating factor μ(t)=e^{\int\limits^  {}k \, dt } =e^{kt}. We now multiply both sides of the equation by the integrating factor.

μv' + μkv = μg ⇒ e^{kt}v' + ke^{kt}v = ge^{kt} ⇒ [ve^{kt}]' = ge^{kt}. Integrating, we have

∫ [ve^{kt}]' = ∫ge^{kt}

    ve^{kt} = \frac{g}{k}e^{kt} + c

    v(t)=   \frac{g}{k} + ce^{-kt}.

From our initial conditions, v(0) = 9.55 m/s, t = 0 , g = 9.8 m/s², γ = 9 kg/s , m = 15 kg. k = y/m. Substituting these values, we have

9.55 = 9.8 × 15/9 + ce^{-16.33 * 0} = 16.33 + c

       c = 9.55 -16.33 = -6.78.

So, v(t)=   16.33 - 6.78e^{-16.33t}. m/s = - 6.78e^{-16.33t} + 16.33 m/s

b. Velocity of object at time t = 0.5

At t = 0.5, v = - 6.78e^{-16.33 x 0.5} + 16.33 m/s = 16.328 m/s ≅ 16.33 m/s

You might be interested in
Baesed on a poll conducted by city council, 700 people voted against a tax policy. Based on the graph how many people voted? 70%
Vinil7 [7]
I would say do 70 percent of the 700 people then do 25 percent then 5 percent
5 0
3 years ago
How many solutions does the equation −2a + 2a + 7 = 8 have? One Two None Infinitely many
aleksandrvk [35]

Answer:

no solutions

Step-by-step explanation:

−2a + 2a + 7 = 8

Combine like terms

7 = 8

This is never true so there are no solutions

5 0
3 years ago
Read 2 more answers
4х + Зу = 9<br> find the slope and y intercept
Volgvan

Step-by-step explanation:

3y/3=9-4x/3

y=3-4x/3

slope=x= -4/3

y intercept

y=3-4(0)/3

y=3-0

y=3

7 0
3 years ago
Help need the answer quick
Shalnov [3]

Answer:

1A

2H

3D

4C

5G

6E hope this helps

6 0
3 years ago
Who knows the Babylonian method, and can help me!<br> **see picture below**
PSYCHO15rus [73]
This is an iteration method for finding the square root.

The ? is also your first initial guess.

? = 10.5

The iteration formula for the square root is actually.

√n =      (x + n/x)÷2.

Where x is your guess.
3 0
3 years ago
Other questions:
  • The product of twice a number and two is the same as the difference of three times the number and 1/2. find the number.
    5·1 answer
  • $8050 invested for 5 years at 4.8% p.a
    11·1 answer
  • Charlie and 10 friends are planning for a pizza party. They purchased 3 quarts of milk. If each glass holds 8oz how much milk wi
    13·2 answers
  • A study is conducted to see how effective aspirin is in reducing temperature in children. A sample of 6 children suffering from
    8·1 answer
  • Find the exact value of sec 3pi/2<br> If not defined, write undefined.
    10·1 answer
  • Bobby and Gautham each save the same amount of money from each lawn they mow. What must be true for Gautham to have more money t
    14·1 answer
  • If it takes 4 years for an animal population to double, how many years will it take until the population triples?
    5·2 answers
  • If the price of a yo-yo in a shop increased by 20% and is now $3.60, what was the original price?
    8·1 answer
  • Simplify this algebraic expression completely 5y - 3(y+2)
    15·1 answer
  • Write in word form: 5,278.081
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!