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
alexira [117]
2 years ago
10

Wonder Woman and Superman fly to an altitude of 1690 km , carrying between them a chest full of jewels that they intend to put i

nto orbit around Earth. They want to make this tempting treasure inaccessible to their evil enemies who are trying to gain possession of it, yet keep it available for themselves for future use when they retire and settle down. But perhaps the time to retire is now! They accidentally drop the chest, which leaves their weary hands at rest, and discover that they are no longer capable of catching it as it falls into the Pacific Ocean. At what speed does the chest impact the surface of the water? Ignore air resistance, although in the real world it would make a world of difference. The radius and mass of Earth are 6370 km and 5.98×1024 kg , respectively.
Physics
1 answer:
Arturiano [62]2 years ago
3 0

Answer:

5120 m/s

Explanation:

The acceleration due to gravity is:

g = MG / r²

where M is the mass of the earth, G is the universal constant of gravitation, and r is the distance from the earth's center to the object's center.

Here, r = h + R, where h is the height of the chest above the surface and R is the radius of the earth.

g = MG / (h + R)²

Acceleration is the derivative of velocity:

dv/dt = MG / (h + R)²

Using chain rule, we can say:

(dv/dh) (dh/dt) = MG / (h + R)²

(dv/dh) v = MG / (h + R)²

Separate the variables:

v dv = MG / (h + R)² dh

Integrating:

∫₀ᵛ v dv = MG ∫₀ʰ dh / (h + R)²

½ v² |₀ᵛ = -MG / (h + R) |₀ʰ

½ (v² − 0²) = -MG / (h + R) − -MG / (0 + R)

½ v² = -MG / (h + R) + MG / R

½ v² = MGh / (R(h + R))

v² = 2MGh / (R(h + R))

Given:

M = 5.98×10²⁴ kg

R = 6.37×10⁶ m

h = 1.69×10⁶ m

G = 6.67×10⁻¹¹ m³/kg/s²

Plugging in:

v² = 2 (5.98×10²⁴) (6.67×10⁻¹¹) (1.69×10⁶) / ((6.37×10⁶) (1.69×10⁶ + 6.37×10⁶))

v² = 2 (5.98) (6.67) (1.69) / ((6.37) (1.69 + 6.37)) × 10⁷

v ≈ 5120 m/s

Notice that if we had approximated g as a constant 9.8 m/s², we would have gotten an answer of:

v² = v₀² + 2a(x - x₀)

v² = (0 m/s)² + 2 (9.8 m/s²) (1.69×10⁶ m - 0 m)

v ≈ 5760 m/s

So we know that our calculated velocity of 5120 m/s is a reasonable answer.

You might be interested in
What is sound wave and examples
Nezavi [6.7K]

<em>★</em><em> </em><em>«</em><em> </em><em><u>what is sound wave and examples</u></em><em><u> </u></em><em>»</em><em> </em><em>★</em>

  • <em>A sound wave is the pattern of disturbance caused by the movement of energy traveling through a medium (such as air, water, or any other liquid or solid matter) as it propagates away from the source of the sound. The source is some object that causes a vibration, such as a ringing telephone, or a person's vocal chords.</em>

<em>hope </em><em>it</em><em> helps</em>

3 0
3 years ago
How many times did john glenn orbit the earth
galben [10]

Answer:

2 times

Explanation:

1st time on Feb. 20, 1962 at age 41

2nd time on Oct. 29, 1998 at age 77

8 0
3 years ago
A woman falls to the ground while wearing a parachute. The air resistance on the parachute of the parachute is 500N. If the woma
scoundrel [369]

The gravitational force on the woman is A) 500 N

Explanation:

There are two forces acting on the woman during her fall:

  • The force of gravity, F_G, acting downward
  • The air resistance, F_D, acting upward

According to Newton's second law, the net force acting on the woman is equal to the product between the woman's mass and her acceleration:

\sum F=ma

where m is the mass of the woman and a her acceleration.

The net force can be written as

\sum F = F_G - F_D

Also, we know that the woman falls at a constant velocity (5 m/s), this means that her acceleration is zero:

a=0

Combining the equations together, we get:

F_G-F_D = 0

which means that the magnitude of the gravitational force is equal to the magnitude of the air resistance:

F_G=F_D=500 N

Learn more about forces and Newton's second law:

brainly.com/question/3820012

#LearnwithBrainly

5 0
2 years ago
Read 2 more answers
A person kicks a 4.0-kilogram door with a 48-newton force causing the door to accelerate at 12 meters per second squared. What i
inna [77]

Answer:

-48 N

Explanation:

mass of door (m) = 4 kg

acceleration of the door = 12 m/s^{2}

force exerted by the person = 48 N

From Newton's third law of motion, action and reaction are equal but opposite. Therefore the force exerted on the door by the person which is 48 N will be the same as the force exerted on the person by the door but opposite in its direction, and this would be - 48 N

7 0
3 years ago
5. How much heat is generated when an
Mila [183]

Answer:

I HOPE THIS IS CORRECT

Explanation:

Power of water =2 kw=2000w

Mass of water =200kg

difference in temperature ΔT=70−10=60oC

Concept

energy required to heat the water = energy given by water in time t=pt

energy required to increase tempeature of water by 60oC,Q=msΔT

S= specific heat =4200J/kgoC

              pt=msΔT

   2000×t=200×4200×60

      t=25200  

or   t=25.2×103sec.

6 0
3 years ago
Other questions:
  • If the coefficient of static friction between your friend and the car seat is 0.500 and you keep driving at a constant speed of
    10·1 answer
  • A theory was not originally a hypothesis. true or false?
    7·1 answer
  • A 3.00 kg object is fastened to a light spring, with the intervening cord passing over a pulley. The pulley is frictionless, and
    15·1 answer
  • Mrs. Buckley asked her physical science class to look at the graph and tell which of the following explanations are most likely
    14·2 answers
  • ? If you are not moving, Newton's First Law says you<br>will...​
    13·1 answer
  • We are usually not aware of the electric force acting between two everyday objects because
    13·2 answers
  • Curves on some test tracks and race courses, such as the Daytona International Speedway in Florida, are very steeply banked.
    11·1 answer
  • PLS ANSWER DUE LATER TODAY!!!
    9·1 answer
  • Which word best completes the sentence?
    11·1 answer
  • Thinking about planck's law, which star would give off the most orange light?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!