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
Ber [7]
3 years ago
12

For a projectile launched from the vertically from the surface the earth with initial velocity v0, the velocity of the projectil

e when at distance r from the center of the earth satisifes the equation:
v^2 = v0^2 + k^2(1/r - 1/R)

Here, k is a positive constant.
Write the differential equation governing the distance r(t)
Physics
1 answer:
UNO [17]3 years ago
3 0

Answer:

(dr/dt) = √(v₀² + k²/r - k²/R)

Explanation:

v² = v₀² + k²[(1/r) - (1/R)]

v = velocity of Body launched from the surface of the earth

v = initial velocity of body

k = a constant

r = distance from the centre of the earth

R = radius of the earth

v² = v₀² + k²/r - k²/R

v = √(v₀² + k²/r - k²/R)

But v = dr/dt

(dr/dt) = √(v₀² + k²/r - k²/R)

(dr/√(v₀² + k²/r - k²/R)) = dt

To go one step beyond and integrate the differential equation

∫ (dr/√(v₀² + k²/r - k²/R)) = ∫ dt

Integrating the left hand side from 0 to r and the right hand side from 0 to t

Note, v₀, k and R are all constants

(- 4r²/k²)[√(v₀² + k²/r - k²/R)] = t

√(v₀² + k²/r - k²/R) = (- k² t/4r²)

(v₀² + k²/r - k²/R) = (- k² t/4r²)²

(v₀² + k²/r - k²/R) = (k⁴t²/16r⁴)

(k⁴t²/16r⁴) + (k²/r) = [v₀² - (k²/R)]

k² [(k²t²/16r⁴) + (1/r)] = [v₀² - (k²/R)]

[(k²t²/16r⁴) + (1/r)] = [(v₀²/k²) - (1/R)]

You might be interested in
A copper wire 20 m long and 4mm in diameter is attached to the Ceiling and a 400 N
Fiesta28 [93]

Answer:

A

Explanation:

5 0
2 years ago
A wooden block has a mass of 562 g and a volume of 72 cm3. What is the density?
dangina [55]
Mass/volume is density so it’s 562g/72cm^3 so it’s roughly 7.805g per cubic centimeter
3 0
3 years ago
Read 2 more answers
If the wave represents a sound wave, explain how increasing amplitude will affect the loudness of the sound? If we decrease the
Viktor [21]

Answer:

Explanation:

Think of a sound wave like a wave on the ocean, or lake... It's not really water moving, as much as it's energy moving through the water. Ever see something floating on the water, and notice that it doesn't come in with the wave, but rides over the top and back down into the trough between them? Sound waves are very similar to that. If you looked at a subwoofer speaker being driven at say... 50 cycles a second, you'd actually be able to see the speaker cone moving back and forth. The more power you feed into the speaker, the more it moves back and forth, not more quickly, as that would be a higher frequency, but further in and further out, still at 50 cycles per second. Every time it pushed out, it's compressing the air in front of it... the compressed air moves away from the speaker's cone, but not as a breeze or wind, but as a wave through the air, similar to a wave on the ocean

More power, more amplitude, bigger "wave", louder ( to the human ear) sound.

If you had a big speaker ( subwoofer ) and ran a low frequency signal with enough power in it, you could hold a piece of paper in front of it, and see the piece of paper move in and out at exactly the same frequency as the speaker cone. The farther away from the speaker you got, the less it'd move as the energy of the sound wave dispersed through the room.

Sound is a wave

We hear because our eardrums resonates with this wave I.e. our ear drums will vibrate with the same frequency and amplitude. which is converted to an electrical signal and processed by our brain.

By increasing the amplitude our eardrums also vibrate with a higher amplitude which we experience as a louder sound.

Of course when this amplitude is too high the resulting resonance tears our eardrums so that they can't resonate with the sound wave I.e. we become deaf

6 0
2 years ago
In 1996, astronomers discovered an icy object beyond pluto that was given the designation 1996 tl 66. it has a semimajor axis of
antoniya [11.8K]

Answer : 2446 years.

Explanation :

Length of semi major axis is, a=84\ au= 1.496\times 10^{11}\ m

According to Kepler's third law, square of time period of an orbit is directly proportional to the cube of the semi major axis.

i.e T^2=\dfrac{4\pi^2}{GM}a^3

where G is gravitational constant

M is  mass of sun, M=1.98\times 10^{30}\ Kg

So, T^2=\dfrac{4\times (3.14)^2}{6.6\times 10^{-11}Nm^2/Kg\times 1.98\times 10^{30}\Kg}

T^2=3\times 10^{-19}\times(84\times 1.496\times 10^{11})^3

T^2=3\times 10^{-19}\times 1984415.6\times 10^{33}

T^2=59532469.8\times 10^{14}\ s

T=7715.7\times 10^7\ s

since, 1\ sec=3.17\times 10^{-8}\ years

So, orbital period is approximately 2446 years.

7 0
3 years ago
Calculate the change in length of a 90.5 mm aluminum bar that has increased in temperature by from -14.4 oC to 154.6 oC
nignag [31]

Answer:

 ΔL = 3.82 10⁻⁴ m

Explanation:

This is a thermal expansion exercise

          ΔL = α L₀ ΔT

          ΔT = T_f - T₀

where ΔL is the change in length and ΔT is the change in temperature

Let's reduce the length to SI units

          L₀ = 90.5 mm (1m / 1000 mm) = 0.0905 m

let's calculate

          ΔL = 25.10⁻⁶ 0.0905 (154.6 - (14.4))

          ΔL = 3.8236 10⁻⁴ m

     

using the criterion of three significant figures

          ΔL = 3.82 10⁻⁴ m

5 0
2 years ago
Other questions:
  • A car traveling at 30m/s screeches to a halt, leaving 55 m long skid marks. what was the cars acceleration while braking
    12·1 answer
  • Which of the following describes the efficiency of real machines?
    13·2 answers
  • PLEASE HELPPPPP!!Calculate the net force acting on obiect A. In your answer, be sure to include the number, unit, and
    8·1 answer
  • How do you identify the zero reference position for calculating mechanical potential energy? What is the most common zero refere
    8·1 answer
  • A piece of fruit falls straight down. As it falls,
    9·1 answer
  • For a medium to transmit a wave, the medium must _____.
    8·1 answer
  • I’m carbon cycle, CO2 is mainly stored in
    14·1 answer
  • Tell me pls<br>question: one way to protect property from damage. (hurricane) (hurricane)​
    6·2 answers
  • If someone were to drop an orb from a height of 34,000 meters approximately, and then drop a second orb at 34,100 meters, estima
    9·1 answer
  • 34 A metal displaces 5.0 cm3 of water when it is totally immersed. If the mass of the metal is 35.0 g, calculate its density A:
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!