<span>The 3rd astronaut would catch the 2nd astronaut and throw the 2nd astronaut towards the 1st and the game would end there.
The key thing to remember is conservation of momentum. Since all of the astronauts have the same mass and strength, I will be introducing a unit called "A" which represents the maximum momentum that one astronaut can produce while throwing another. So here's the game of catch, throw by throw.
Before the game begins, I will assume all three astronauts are stationary and have 0 momentum. So
Astronaut 1 = 0 A (Stationary, next to astronaut 2)
Astronaut 2 = 0 A (Stationary, next to astronaut 1)
Astronaut 3 = 0 A (Stationary)
1st astronaut grabs the 2nd astronaut and throws him towards the 3rd.
Since every action has an equal and opposite reaction, what will happen is the 1st astronaut will be sent moving backwards with a momentum of -1/2A and the 2nd astronaut will be heading towards the 3rd with a momentum of +1/A. So we're left with
Astronaut 1 = -1/2 A (Moving to the left)
Astronaut 2 = +1/2 A (Moving to the right)
Astronaut 3 = 0 A (Stationary)
Now the 3rd astronaut catches the 2nd who was thrown at him. Both of them continue moving in the same direction as the 2nd astronaut was just prior to being caught, but at a reduced velocity, giving
Astronaut 1 = -1/2 A (Moving to the left)
Astronaut 2 = +1/4 A (Moving to the right, slowly)
Astronaut 3 = +1/4 A (Moving to the right, slowly)
Finally, Astronaut 3 throws astronaut 2 back towards Astronaut 1, giving
Astronaut 1 = -1/2 A (Moving to the left)
Astronaut 2 = +1/4 A -1/2A = -1/4A (Moving to the left, slowly)
Astronaut 3 = +1/4 A +1/2A = +3/4A (Moving to the right, rapidly)
So what you're left with is Astronaut 1 moving to the left faster than Astronaut 2, so those two astronauts will never catch each other. Meanwhile, Astronaut 3 is moving to the right and getting further and further away from the other 2 astronauts. So none of the astronauts will ever be able to catch or throw anyone ever again.</span>
Answer: Choice A
Step-by-step explanation:
Answer:
d(63)=21,420m
Step-by-step explanation:
d(t)=340t
D=Distance
T=Time
D(63)=21,420
Answer:
See explanation
Step-by-step explanation:
1. Make sure that the trinomial is written in the correct order - the trinomial must be written in descending order from highest power to lowest power. In you case, the trinomial must be written as
2. Decide if the three terms have anything in common, called the greatest common factor or GCF. If so, factor out the GCF. Do not forget to include the GCF as part of your final answer.
In your case, coefficients 2, 5 and 3 do not have common factors, so go to the next step.
3. Multiply the leading coefficient and the constant, that is multiply the first and last numbers together:
4. List all of the factors from step 3 and decide which combination of numbers will combine to get the number next to x:
5. After choosing the correct pair of numbers, you must give each number a sign so that when they are combined they will equal the number next to x and also multiply to equal the number found in Step 3:
6. Rewrite the original problem with four terms by splitting the middle term into the two numbers chosen in step 5:
7. Now that the problem is written with four terms, you can factor by grouping:
