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
gogolik [260]
3 years ago
14

A spaceship maneuvering near planet zeta is located at r⃗ =(600i^−400j^+200k^)×103km, relative to the planet, and traveling at v

⃗ =9500i^m/s. it turns on its thruster engine and accelerates with a⃗ =(40i^−20k^)m/s2 for 35 min. part a what is the spaceship's position when the engine shuts off? give your answer as a vector measured in km.
Physics
2 answers:
Sedaia [141]3 years ago
7 0

The position of the spaceship as the engine shuts off is given as \boxed{x=(708.15\,\hat{i}-400\,\hat{j}+155.9\,\hat{k})\times10^3\text{ km}}.

Explanation:

Given:

The initial position of the spaceship relative to the planet is (600\,\hat{i}-400\,\hat{j}+200\,\hat{k})\times10^3\text{ km}.

The speed of the spaceship is 9500\,\hat{i}\text{ m/s}.

The acceleration of the spaceship is 40\,\hat{i}-20\,\hat{k}\text{ m/s}^2.

The time for which the thruster engine accelerates the spaceship is 35\text{ min}.

Concept:

As the spaceship is accelerated by the thruster engine, the spaceship moves according to the second equation of motion.

Write the expression for the displacement of the spaceship in time interval.

\boxed{S=v_{o}t+\dfrac{1}{2}at^2}

Here, S is the total displacement of the spaceship, v_{o} is the initial velocity of spaceship, a is the acceleration of the spaceship and t is the time for which the spaceship accelerates.

Substitute the values of the initial speed, acceleration and the time taken by the spaceship in above expression.

\begin{aligned}S&=\{9500\,\hat{i}\times(35\times60)\}+\dfrac{1}{2}(40\,\hat{i}-20\,\hat{k})(35\times60)^2\\&=(1.995\times10^7\,\hat{i})+(8.82\times10^7)\,\hat{i}-(4.41\times10^7)\,\hat{k}\\&=(108.15\,\hat{i}-44.1\,\hat{k})\times10^6\text{ m}\\&=(108.15\,\hat{i}-44.1\,\hat{k})\times10^3\text{ km}\end{aligned}

Write the expression for the new position of the spaceship after it stops.

X'=X_{o}+S

Substitute the value of the initial position and the displacement of the spaceship.

\begin{aligned}X'&=(600\,\hat{i}-400\,\hat{j}+200\,\hat{k})\times10^3\text{ km}+(108.15\,\hat{i}-44.1\,\hat{k})\times10^3\text{ km}\\&=(708.15\,\hat{i}-400\,\hat{j}+155.9\,\hat{k})\times10^3\text{ km}\end{aligned}

Thus, the position of the spaceship as the engine shuts off is given as \boxed{x=(708.15\,\hat{i}-400\,\hat{j}+155.9\,\hat{k})\times10^3\text{ km}}.

Learn More:

1. A car's position in relation to time is plotted on the graph. what can be said brainly.com/question/11314764

2. Vector a points in the negative y direction and has a magnitude of 5 km brainly.com/question/1511269

3. The position of a 55 g oscillating mass is given by brainly.com/question/4544154

Answer Details:

Grade: High School

Subject: Physics

Chapter: Scalar and Vector

Keywords:

spaceship, maneuvering, planet zeta, travelling, thruster, displacement, acceleration, initial velocity, engine, time, position.

slava [35]3 years ago
3 0

<u>Answer:</u>

 The spaceship's position when the engine shuts off = (708.15 i - 444.1 j + 200 k)*10^3km

<u>Explanation:</u>

  Initial location of spaceship = (600 i - 400 j + 200 k)*10^3km= (600 i - 400 j + 200 k)*10^6m

  Initial velocity = 9500 i m/s

  Acceleration = (40 i - 20 k)10^3m/s^2

  Time = 35 minute = 35 * 60 = 2100 seconds

 We have equation of motion , s= ut+\frac{1}{2} at^2, s is the displacement, u is the initial velocity, a is the acceleration and t is the time.

  Substituting

       s= (9500 i)*2100+\frac{1}{2}*(40 i - 20 k)*2100^2\\ \\ s=9500*2100 i+20*2100^2i-10*2100^2j\\ \\ s=19.95*10^6i+88.2*10^6i-44.1*10^6j\\ \\ \\s=(108.15i-44.1j)*10^6m

     So final position = ((600 i - 400 j + 200 k)+(108.15i-44.1j))*10^6=(708.15 i - 444.1 j + 200 k)*10^6m

                              =(708.15 i - 444.1 j + 200 k)*10^3km

    The spaceship's position when the engine shuts off = (708.15 i - 444.1 j + 200 k)*10^3km

You might be interested in
In a real system of levers, wheels, or pulleys, the AMA is less than the IMA because _____.
grandymaker [24]
In a real system of levers, wheel or pulleys, the AMA (actual mechanical advantage) is less than the IMA (ideal mechanical advantage) because of the presence of friction.

In fact, the IMA and the AMA of a machine are defined as the ratio between the output force (the load) and the input force (the effort):
IMA= \frac{F_{out}}{F_{in}}
however, the difference is that the IMA does not take into account the presence of frictions, while the AMA does. As a result, the output force in the AMA is less than the output force in the IMA (because some energy is dissipated due to friction), and the AMA is less than the IMA.
5 0
3 years ago
Read 2 more answers
Can someone help me with science
tamaranim1 [39]
The continuious physical force per unit area that one region of a gas, liquid, or solid exerts on another.
6 0
3 years ago
In an adiabatc process, what happens when gases in a system are compressed?
likoan [24]

Answer:work is done, and temperature increases

Explanation:

In an adiabatic process, when gases are compressed, work is done on the liquid and the temperature increases

8 0
3 years ago
How many atoms of carbon would two molecules of glucose (C6H12O6) have?
Sauron [17]
Well according to the molecular formula of glucose, one molecule would have 6 carbon atoms, and thus 2 molecules of glucose would have 12 carbon atoms.

The correct response would be B. 12.
4 0
3 years ago
Read 2 more answers
A student asks the following question:
MariettaO [177]

Answer:

  Natalie says that all things with mass have a gravitational field, but the force is very weak and cannot be perceived around small objects.

Explanation:

The force due to gravity is proportional to the mass of the object and inversely proportional to the square of the distance between objects. The Earth is so massive that the force due to its gravity is much greater than the force between objects on the counter.

If there were no friction, the objects might move toward each other, depending on what other masses were near them tending to cause them to move in other directions.

Natalie's explanation is about the best.

__

<em>Additional comment</em>

The universal gravitational constant was determined by Henry Cavendish in the late 18th century using lead balls weighing 1.6 pounds and 348 pounds. His experiment was enclosed in a large wooden box to minimize outside effects. While these masses are somewhat greater than those of a glue bottle and stapler, the experiment shows the force of gravity between "small" objects <em>can</em> be measured.

8 0
3 years ago
Other questions:
  • How many total atoms are in one molecule of lithium nitrate, LiNO3? 1 3 5 7 6
    9·2 answers
  • A child in danger of drowning in a river is being carried down-stream by a current that flows uniformly with a speed of 2.20 m/s
    10·1 answer
  • How will heat flow between objects?
    10·2 answers
  • Do you think scientists will ever be able to recreate a living creature from the distant past successfully?
    8·2 answers
  • Different masses are hung on a spring scale calibrated in newtons. The force exerted by gravity on 1.0 kg is shown in the image
    6·2 answers
  • Leila drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10 hours. When Leila drov
    13·1 answer
  • During a circus act, one performer swings upside down hanging from a trapeze holding another, also upside-down, performer by the
    8·1 answer
  • A bird is flying in a room with a velocity field of . Calculate the temperature change that the bird feels after 9 seconds of fl
    10·1 answer
  • These has two questions, any help would be much appreciated. Ignore the current answers.
    11·1 answer
  • A centrifuge in a medical laboratory rotates at an angular speed of 3,400 rev/min. When switched off, it rotates through 52.0 re
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!