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
liberstina [14]
3 years ago
5

A piano is hauled into space a distance 3 earth radii above the surface of the north pole and is then dropped. About how long wi

ll it take to splash down in the arctic ocean
Mathematics
1 answer:
nikdorinn [45]3 years ago
6 0

Answer:

The answer to the question is

It would take about 167.021 s  to splash down in the arctic ocean.

Step-by-step explanation:

The gravitational force is given by

F_G = \frac{G*m_1*m_2}{r^2}

Where m₁ mass of the piano and

m₂ = mass of the Earth

r = 3·R where R = radius of the earth

as stated in the question we have varying acceleration due to the inverse square law

Therefore at 3 × Radius of the earth we have

F_G = 109.083 N and the acceleration =1.09083 m/s²

If the body falls from 3·R to 2·R with that acceleration we have

S = u·t +0.5×a·t²  = 0.5×a·t² as u = 0

That is 6371 km = 0.5·1.09083·t²

t₁ = 108.079 s and we have

v₁² = u₁² +2·a₁·s₁ =  2·a₁·s₁ = 117.895 m/s

For the next stage r₂ = 2R

Therefore F = 245.436 N and a₂ = F/m₁ = 2.45436 m/s²

Therefore the time from 2R to R is given by

S₂ =R=u·t+0.5·a₂·t² = v₁·t + 0.5·a₂·t²

or 6371 km = 117.895 m/s × t + 0.5 × 2.45436 × t²

Which gives 1.22718 × t² + 117.895 × t -6371  = 0

Factorizing we have (t+134.631)(t-38.56)×1.22718 = 0

Therefore t = -134.631 s or 38.56 s as we only deal with positive values of time in the present question we have t₂ = 38.56 s and

v₂² = v₁² + 2·a₂·S  = (117.895 m/s)² + 2·2.45436 m/s²×6371 km = 45172.686

v₂ = 212.54 m/s

For final stage we have r = R and

F_{G3} = 981.746 N and a₂ = F/m₁ = 9.81746 m/s²

Therefore the time from R to the arctic ocean  is given by

S₃ =R=v₂·t+0.5·a₂·t² = 212.54·t + 0.5·9.81746·t² = 6371

Which gives

Therefore t₃ = 20.382 s

Therefore, it will take about t₁ + t₂ + t₃ = 108.079 s + 38.56 s + 20.382 s  = 167.021 s  to splash down in the ocean

You might be interested in
Danielle sells
Xelga [282]
Hello! So a 9% commission is earned on the amount of beauty supplies sold. To find out the amount of commission earned, all you have to do is multiply $895 by 9%. 895 * 9% (0.09) is 80.55. $80.55 is earned in commission, Now, add 450 to that amount. 80.55 + 450 is 530.55. There. Danielle earned a total of $530.55 this week.
7 0
3 years ago
Help me asap plz !!!!!!!!!!!!!!!!!!!
frez [133]

Answer:

The answer will be A. 27f

6 0
3 years ago
Read 2 more answers
F ∝ a If F = 48 when a = 3 find, a when F = 32
LenKa [72]

Answer:

2

Step-by-step explanation:

f = a

48 = 3

32 = x

48x= 98

<u>x=2</u>

<h2><u>Mark me as brainiest if i helped you </u></h2>
4 0
3 years ago
24 question thank you
Alona [7]

You would just do 3/5 * 55 = 33 movies were new releases.

8 0
3 years ago
Read 2 more answers
Simplify and show step by step 30 POINTS!
PIT_PIT [208]

Step-by-step explanation:

the explanation is in the diagram above

4 0
2 years ago
Other questions:
  • Pls help me out!! lol
    9·1 answer
  • Cities A &amp; B are 5 inches apart on a map. Cities C&amp;D are 4 inches apart. If C &amp; D are 900 miles apart, how many mile
    11·1 answer
  • To multiply polynomials, I do what?
    5·1 answer
  • If x= -8 and y=-4​, evaluate the expression.<br> <img src="https://tex.z-dn.net/?f=%5Cfrac%7B3x-4%7D%7By-3%7D" id="TexFormula1"
    5·1 answer
  • What is the correct equation for the line in slope-intercept form?
    10·1 answer
  • Which expression will give a <br> product of 14/9
    11·1 answer
  • Hellllllllllllllllllllp
    12·1 answer
  • A rectangular lawn measuring 24 feet by 16 feet is surrounded by a flower bed of uniform width. The combined area of the lawn an
    15·1 answer
  • What's 4x + 3 = 2x + 17
    9·1 answer
  • Wesley Snipes earns a monthly salary of $1,685, plus a 8.5% commission on all sales over $2,000 each month. This month, his sale
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!