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
Nimfa-mama [501]
3 years ago
13

g A projectile is shot directly away from Earth's surface. Neglect the rotation of the Earth. What multiple of Earth's radius RE

gives the radial distance (from the Earth's center) the projectile reaches if (a) its initial speed is 0.216 of the escape speed from Earth and (b) its initial kinetic energy is 0.216 of the kinetic energy required to escape Earth? (Give your answers as unitless numbers.) (c) What is the least initial mechanical energy required at launch if the projectile is to escape Earth?
Physics
1 answer:
Ann [662]3 years ago
8 0

Answer:

a)   r_{max} = 1,049  R_{e}

, b)   r_{max} = 1,276  R_{e}

Explanation:

For this exercise we must look for the Earth's escape velocity, for this we use the conservation of energy at two points on the surface and one point at a very distant point.

Initial. Earth's surface

      Em₀ = K + U = ½ m v² - G m M / R_{e}

Final. Very far point

       Em_{f} = U = - G m M / r_{max}

Energy is conserved

       Emo =   Em_{f}

       ½ m v² - G m M /R_{e} = - G m M /  r_{max}

       v² = 2 G M (1 / R_{e} - 1 /  r_{max})

The escape velocity is defined as the speed to take the projectile to an infinite distance (r_{max} = ∞)

      v = √ (2GM / R_{e})

In our case the speed is v = 0.216 vesc

Let's clear the maximum height

      1 /  R_{e} - 1 / r_{max} = v² / 2GM

      1 / r_{max} = 1 /  R_{e} - v² / 2GM

We substitute and calculate

       1 / r_{max} = 1 /  R_{e} - 0.216² (2GM / Re) / 2GM

       1 / r_{max} = 1 /  R_{e} - 0.046656 /  R_{e}

       1 / r_{max} = 1 /  R_{e} (1 -0.046656)

        r_{max} =  R_{e} / 0.953344 = 1.049  R_{e}

        r_{max} = 1,049  R_{e}

b) the kinetic energy is 0.216 of the kinetic energy to escape from the earth

Kinetic energy

        K = ½ m vesc²

        K = ½ m 2GM /  R_{e} = A

Where A is the value of the kinetic energy of escape, in our case we have

         0.216 A = ½ m v²

         v² = (0.216 A) 2 / m

We substitute in the equation of maximum height

          1 / r_{max} = 1 /  R_{e} - v² / 2GM

          1 / r_{max} = 1 /  R_{e} - (0.216 A 2/m) / 2GM

We substitute the value of A

          1 / r_{max} = 1 /  R_{e} - 0.216 2/m (1/2 m 2GM /  R_{e}) 1 / 2GM

          1 / r_{max} = 1 /  R_{e} - 0.216 1 /  R_{e}

          1 / r_{max} = 1 /  R_{e} (1-0.216)

           r_{max} =  R_{e} /0.784

           r_{max} = 1,276  R_{e}

c) the initial mechanical energy

The definition of the escape velocity is the speed to take the body to an infinite distance with zero speed, the energy difference is zero

           K = U

          Em = 0

You might be interested in
What does the zigzag line in the circuit diagram represent? A. a source of electrical energy B. an electrical conductor C. an el
lora16 [44]
C. an electrical resistor 
8 0
3 years ago
Read 2 more answers
Who needs to know physics when they are making a satellite
vladimir2022 [97]
First satellite was Sputnik and it was a race then to send satellites!! Everyone starts experimenting how to launch.

first try was on a dog , Laika !! It was send to space as it is long after sputnik is placed in orbit !!

Now you know everyone knows rocket science and the most active are ISRO (India) and NASA (USA) !!
4 0
3 years ago
explain a method applied to test a diesel engine at constant speed at list the method used to measure the friction power​
lana66690 [7]

Automotive idustries  made a paradigm shift in selection of viscometrics of engine lubricant,from higher to lower viscosity grade,for improving fuel economy

Explanation:

3 0
3 years ago
A 3874-kg rollercoaster is brought to the top of a 42m hill in 40 seconds,then drops 28m before the next hill.
Ede4ka [16]

(a) The work required to get the coaster to the top of the first hill is  1,594,538.4 J.

(b) The power required to bring the train to the top of the first hill is 39,863.46 W.

(c) The energy lost when the coaster drops is 531,512.8 J.

(d) The left at the bottom is determined as 1,063,025.6 J.

<h3>Work done to bring the rollercoaster top of the hill</h3>

W = Fn x d = mgh

W = 3874 x 9.8 x 42

W = 1,594,538.4 J

<h3>Power dissipated in bringing the rollercoaster on top hill</h3>

P = Fv

P = Fd/t

P = W/t

P = 1,594,538.4 /40 = 39,863.46 W

<h3>Energy lost when the coaster drops</h3>

E = 1,594,538.4 - (3874 x 9.8 x 28)

E = 531,512.8 J

<h3>Energy left at the bottom</h3>

E = 3874 x 9.8 x 28 = 1,063,025.6 J

Learn more about energy here: brainly.com/question/13881533

#SPJ1

6 0
2 years ago
Classify the animal hydra and plant mustard with two characters of each​
inna [77]

Answer:

Mustard seeds, both white and brown, are nearly globular in shape, finely pitted, odourless when whole, and pungent-tasting

Image result for character of hydra

Introduction: Hydra are inconspicuous freshwater relatives of corals, sea anemones and jellyfish. All are members of the phylum Cnidaria, characterized by radially symmetrical bodies, presence of stinging tentacles and a simple gut with only one opening (gastrovascular cavity)

Explanation:

Hydra are a genus of small, fresh-water organisms that are classified under the phylum Cnidaria.the classification of mustard is

Dicotyledons

if my answer helps you than mark me as brainliest

4 0
3 years ago
Other questions:
  • Please i really need help..
    10·2 answers
  • Give an example of how electrical energy and thermal energy are connected.
    14·1 answer
  • Which of the following best describes what alveolar are
    15·2 answers
  • A metal detector used in airports is actually a large coil of wire carrying a small current. Explain how it detects a gun, even
    10·1 answer
  • if an object exposed to salt water that seeps into cracks and forms crystals what is likely to occur?
    13·1 answer
  • A positively charged particle is located at point A and is stationary. The direction of the magnetic force on the particle is:
    15·1 answer
  • The part of the computer that provides access to the internet is
    13·1 answer
  • Pls help me its due today ​
    11·1 answer
  • What is the speed of a car that travels a distance of 60 meters in a time of 10 seconds
    5·1 answer
  • Give an example of a force applied to an object that does not change the object's velocity. Why does the object's velocity not c
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!