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
Explain why sedimentary rocks are found as a veneer covering large areas of the continental igneous rocks
musickatia [10]
Sedimentary rocks are the result of igneous rocks<span> breaking down.This is a slow process so there is not as much broken down as there is not broken down.</span>
6 0
3 years ago
Read 2 more answers
Newtons laws of motion
Viktor [21]

Answer:

Law 1. A body continues in its state of rest, or in uniform motion in a straight line, unless acted upon by a force.

Law 2. A body acted upon by a force moves in such a manner that the time rate of change of momentum equals the force.

Law 3. If two bodies exert forces on each other, these forces are equal in magnitude and opposite in direction.

7 0
2 years ago
When light generated by a lamp in a light microscope passes into a lens, the speed of the light _______ because the glass lens h
Alina [70]

Answer:

the answer is slows and greater

Hopes it helps!

6 0
3 years ago
A force of 900 N is applied to a 9kg object. How fast will it accelerate?
saul85 [17]

Answer:  15 m/s2

Explanation: I hope this helps or right because I learned this a few months ago

7 0
2 years ago
Read 2 more answers
- In Einstein's famous equation E = me?, describing the
mel-nik [20]

Answer:

option C is correct

Explanation:

8 0
3 years ago
Other questions:
  • If a particle with a charge of +4.3 × 10−18 C is attracted to another particle by a force of 6.5 × 10−8 N, what is the magnitude
    8·1 answer
  • When bonds between atoms are broken or formed, what is the outcome? A. a physical change B. an element increasing in size C. a c
    15·1 answer
  • Which pair of properties apply to both sound and electromagnetic waves?
    12·1 answer
  • Scientists classify rocks by
    7·1 answer
  • Two lasers, one red (with wavelength 633.0 nm) and the other green (with wavelength 532.0 nm), are mounted behind a 0.150-mm sli
    9·1 answer
  • At a country music festival, a band is playing at the end of a crowded
    9·1 answer
  • If your weight is 588N on the earth, how far should you go from the centre of the earth so that your weight will be 300N? The ra
    15·1 answer
  • A man enters a tall tower, needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floo
    14·1 answer
  • You lift a 10-kg box to a height of 1m. How much work do you do on the box when you lift it from the ground? (g= 9.81 m/s2)
    15·1 answer
  • A cross country skier moves 32 m north, then 65 m south, and finally 16 m north. What is the distance? What is the displacement
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!