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
Iteru [2.4K]
3 years ago
10

A rocket is launched straight up from the earth's surface at a speed of 1.80×104 m/s .part awhat is its speed when it is very fa

r away from the earth?
Physics
2 answers:
Neko [114]3 years ago
5 0

The speed of the rocket when it is very far away from the Earth is  \boxed{1.61 \times {{10}^4}\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace} {\text{s}}}}.

Further Explanation:

Since the gravitational potential energy of the rocket will become when the rocket reaches a distance far away from the Earth, the complete kinetic and gravitational potential energy of the rocket on the surface of Earth is converted into the kinetic energy of the rocket.

The total energy of the rocket on the surface of the Earth is:

T{E_i} = {K_i} + {U_i}

Here,  is the kinetic energy of the rocket and {U_i} is the gravitational potential energy of the rocket.  

The kinetic energy of the rocket when it starts from the surface of Earth is:

{K_i} =\dfrac{1}{2}mv_i^2

The total gravitational potential energy of the rocket when it was on the surface of the Earth is:

{U_i}= - \dfrac{{GMm}}{r}

Here, m is the mass of the rocket and M is the mass of the Earth.

The final energy of the rocket will be in the form of the kinetic energy only. The final energy of the rocket will be:

{K_f} =\dfrac{1}{2}mv_f^2

Now, using the conservation of energy for the rocket:

\begin{aligned}T{E_i} &= T{E_f} \hfill\\{K_i} + {U_i} &= {K_f}\hfill\\\frac{1}{2}mv_i^2- \frac{{GMm}}{r}&= \frac{1}{2}mv_f^2 \hfill\\\end{aligned}

Rearrange the above expression for final velocity and substitute the values.

\begin{aligned}{v_f}&= \sqrt {v_i^2 - \frac{{GM}}{r}}\\&= \sqrt {{{\left( {1.80 \times {{10}^4}} \right)}^2} - \frac{{\left( {6.67 \times {{10}^{11}}} \right)\left( {5.97 \times {{10}^{24}}}\right)}}{{6.37 \times {{10}^6}}}}\\&= \sqrt {\left( {3.24 \times {{10}^8}} \right) - \left( {6.25 \times {{10}^7}} \right)}  \\&= 1.61 \times {10^4}\,{{\text{m}} \mathord{\left/{\vphantom {{\text{m}} {\text{s}}}}\right.\kern-\nulldelimiterspace} {\text{s}}}\\\end{aligned}

Thus, the speed of the rocket when it is very far away from the Earth is  \boxed{1.61 \times {{10}^4}\,{{\text{m}}\mathord{\left/ {\vphantom{{\text{m}}{\text{s}}}} \right.\kern-\nulldelimiterspace} {\text{s}}}}

Learn More:

1. Choose the 200 kg refrigerator. Set the applied force to 400 N brainly.com/question/4033012

2. How far must you compress a spring with twice the spring constant to store the same amount of energy brainly.com/question/2114706

3. Calculate the total force on the earth due to Venus, Jupiter, and Saturn brainly.com/question/2887352

Answer Details:

Grade: College

Subject: Physics

Chapter: Gravitation

Keywords:  Rocket, gravitational potential energy, kinetic energy, very far away, Earth, launched straight up, speed of rocket, initial energy, 1.80x10^4 m/s.

balandron [24]3 years ago
3 0
We can solve the problem by using the law of conservation of energy.

When the rocket starts its motion from the Earth surface, its mechanical energy is sum of kinetic energy and gravitational potential energy:
E_i = K_i + U_i =  \frac{1}{2} m v_i^2 + (- \frac{GM}{r} )
where
m is the rocket's mass
v_i = 1.8 \cdot 10^4 m/s is the rocket initial speed
G=6.67 \cdot 10^{-11} m^3 kg^{-1} s^{-2} is the gravitational constant
M=5.97 \cdot 10^{24} kg is the Earth's mass
r= 6.37 \cdot 10^6 m is the distance of the rocket from the Earth's center (so, it corresponds to the Earth's radius)

The mechanical energy of the rocket when it is very far from the Earth is just kinetic energy (because the gravitational potential at infinite distance from Earth is taken to be zero):
E_f = K_f =  \frac{1}{2} mv_f ^2
where v_f is the final speed of the rocket.

By equalizing the initial energy and the final energy, we can find the final velocity:
\frac{1}{2} mv_i ^2 -  \frac{GM}{r} = \frac{1}{2}m v_f^2
v_f =  \sqrt{v_i^2 -  \frac{GM}{r} } =1.41 \cdot 10^4 m/s
You might be interested in
A jet taxiing down the runway receives word that it must return to the gate. The jet is traveling 37.6 m/s when the pilot receiv
IrinaVladis [17]

Answer:

7 m/s^2

Explanation:

Given that the jet is traveling 37.6 m/s when the pilot receives the message. 

And it takes the pilot 5.37 s to bring the plane to a halt.

Acceleration of the plane can be calculated by using first equation of motion

V = U - at

Since the plane is going to stop, the final velocity V = zero.

And the acceleration will be negative

Substitute all the parameters into the formula

0 = 37.6 - 5.37a

5.37a = 37.6

Make a the subject of formula

a = 37.6 / 5.37

a = 7.0 m/s^2

Therefore, the acceleration of the plane to bring the plane to a halt is 7 m/s^2

5 0
3 years ago
What is cosmic ray spallation
love history [14]

The Cosmic Ray is a natural way for nuclear fission and nucleosynthesis to occur. It refers to the formation of chemical elements from the impact of cosmic rays on an object.

6 0
3 years ago
Read 2 more answers
A professional golfer hits a golf ball of mass 46 g with her 5-iron, and the ball first strikes the ground 155 m away. The ball
RideAnS [48]

Answer:

C=2.32\times 10^{-4}\ Ns^2/m^2

Explanation:

It is given that,

Mass of the golf ball, m = 46 g = 0.046 kg

Terminal speed of the ball, v = 44 m/s

The drag force, F_r=Cv^2

Where, C is the drag coefficient. At terminal speed, the weight of the ball is balanced by the drag force.

Cv^2=mg

C=\dfrac{mg}{v^2}

C=\dfrac{0.046\times 9.8}{(44)^2}

C=2.32\times 10^{-4}\ Ns^2/m^2

Hence, this is the required solution.

4 0
3 years ago
Which runner has greater kinetic energy: a 45 kg runner moving at a speed of 7 m per second or a 93 kg runner moving at a
bagirrra123 [75]

Kinetic Energy = (1/2) (mass) (speed)

First runner:  KE = (1/2) (45kg) (49 m/s)  =  1,102.5 Joules  

Second runner:  KE = (1/2) (93kg) (9 m/s)  =  418.5 Joules

The <em>first runner </em><em>has 163</em>% more kinetic energy than the second runner has.

7 0
3 years ago
15 PTS! HELP! BRAINLIEST!
vodka [1.7K]
I cant do all but I can do number 4
      When force moves ur leg u start skatin and when that happenes ur using a lot of force to move
3 0
3 years ago
Other questions:
  • If a refrigerator is a heat pump that follows the first law of thermodynamics, how much heat was removed from food inside of the
    12·1 answer
  • Explain how convection currents help mushrooms reproduce. Which spheres are interacting in this example?
    12·1 answer
  • A 60 kg runner in a sprint moves at 11 m/s. A 60 kg cheetah in a sprint moves at 33 m/s. By what factor does the kinetic energy
    7·2 answers
  • The concentration of carbon monoxide in an urban apartment is 48μg/m3. What mass of carbon monoxide in grams is present in a roo
    5·1 answer
  • Give the atomic mass and atomic number of this atom.
    15·1 answer
  • 1/12 of 1/3 is what fraction?
    8·1 answer
  • Which avtivties belongs on top of physical activity pyramid
    15·2 answers
  • Can you make sunglasses from new 3D-glasses???
    13·2 answers
  • The shaded boxes contain the first half of four statements. The unshaded boxes
    15·1 answer
  • Consider the following scenario. A car for which friction is not negligible accelerates from rest down a hill, running out of ga
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!