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
Suppose that two point charges, each with a charge of +1.00 C, are separated by a distance of 1.0 m. If the distance between the
Aleksandr-060686 [28]

Given:

The magnitude of each charge is q1 = q2 = 1 C

The distance between them is r = 1 m

To find the force when distance is doubled.

Explanation:

The new distance is

\begin{gathered} r^{\prime}=\text{ 2r} \\ =2\times1 \\ =2\text{ }m \end{gathered}

The force can be calculated by the formula

F=k\frac{q1q2}{(r^{\prime})^2}

Here, k is the constant whose value is

k=9\times10^9\text{ N m}^2\text{ /C}^2

On substituting the values, the force will be

\begin{gathered} F=9\times10^9\times\frac{1\times1}{(2)^2} \\ =2.25\times10^9\text{ N} \end{gathered}

7 0
1 year ago
A 20-cm long spring is attached to the wall. When pulled horizontally with a force of 100N, the spring stretches to a length of
suter [353]

Answer:

Explanation:

Part 0

All the spring moves is 2 cm

x = 2 cm * [1 m / 100 cm ]

x = 0.020 meters

F = k*d

100N = k * 0.02 m

100 N / 0.02 = k

5000 N / m

Part A

The spring feels a force of 100 N - - 100N = 200 N because each person is pulling in the opposite direction.

F = k * x

200N = 5000 N/m * d

200 / 5000 = d

d = 0.04 meters.

Part B

10.2 kg must be converted to a force as experienced here on earth.

F = m * g

g = 9.81

m = 10.2

F = 10.2 * 9.81

F = 100.06 N

F = k * d

100.06 = 5000 * d

d = 100.06 / 5000

d = 0.02 meters.

3 0
3 years ago
A dog barking at the sound of the postal carrier delivering mail is reacting to what type of cue?
Gwar [14]

Answer:

A. External

Explanation:

External stimulus includes touch/pain, vision, smell, taste, and sound.

6 0
2 years ago
The fire alarm goes off, and a 75 kg firefighter slides down a pole with a constant acceleration of a = 6 m/s square. What is th
Alex17521 [72]

Answer:

450N

Explanation:

Given data

Mass m= 75kg

Acceleration= 6m/s^2

From the Newtons first law, F=ma

substitute

F=75*6

F= 450N

Hence the force is 450N

3 0
3 years ago
The Capacitive reactance of a 0.094uF capacitor when a frequency of 25kHz is applied is lus 68 Ohms 0.68 Ohms luf
Nana76 [90]

Answer:

Capacitive reactance of the capacitor is 68 ohms

Explanation:

It is given that,

Capacitance, C=0.094\ \mu F=0.094\times 10^{-6}\ F

Frequency, f=25\ kHz=25\times 10^3\ Hz

Capacitive reactance is given by :

X_C=\dfrac{1}{2\pi fC}

X_C=\dfrac{1}{2\pi 25\times 10^3\times 0.094\times 10^{-6}}

X_C=67.72\ \Omega

or

X_C=68\ \Omega

So, the capacitive reactance of the capacitor is 68 ohms. Hence, this is the required solution.

8 0
3 years ago
Other questions:
  • Air compressed in car engine from 25 C and 100 kPa in reversible and adiabatic manner. If the compression ratio = 9.058, determi
    5·1 answer
  • A wooden block has a mass of 20.0 kg and a specific heat of 1700 J/kg °C. Find the change in thermal energy of the block as it w
    10·1 answer
  • How does a radiosonde can be used to predict future weather conditions in a location?
    9·1 answer
  • A rock is dropped from a tower 70.0 m high. How long does it take for the rock to hit the ground?​
    14·1 answer
  • Which statement is most likely correct?
    8·2 answers
  • A particle of mas 0.1 kg moves along the trajectory x(t)-3t t where x is in meters and t is in seconds. What is the kinetic ener
    8·1 answer
  • What is the heart rate recorded a few minutes after completing a workout?
    6·2 answers
  • Why might a telescope be built high in the mountains above weather sys
    8·2 answers
  • Projectiles move in which two directions?
    13·2 answers
  • How can you use a simple model to describe a wave and its features?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!