Momentum questions--need them done tonight

[manjuj]

Please help with the following 3 questions:

1. A group of playful astronauts each with a bag full of balls, form a circle as they free fall in space. Describe what happens when they begin tossing the balls simultaneously to one another.

Due to absence of gravitation, wouldn't the balls be floating away - but this seems to be a laymans answer and I do not think its correct.

2. A 5-kg fish swimming 1 m/s swallows an absent minded 1 kg fish at rest. What is the speed of the larger fish immediately after lunch? What would its speed be if the small fish were swimming toward it at 4 m/s?

After lunch:
m(1)=5 kg, v(1)=1 m/s, m(2)=1 kg, v(2)=0

(5)(1) + (1)(0)
--------------- = 5/6 m/s
(5)+(1)

If small fish swimming toward it at 4 m/s:

m(1)=5 kg, v(1)=1 m/s, m(2)=1 kg, v(2)=-4 m/s (swimming towards it)

(5)(1) + (1)(-4)
--------------- = 1/6 m/s
(5)+(1)

3. Comic strip hero Superman meets an asteroid in outer space and hurls it at 100 m/s. The asteroid is on thousand times more massive than superman is. In the strip, superman is seen at rest after the throw. Taking physics into account, what would be his recoil speed?

This question has been asked before by someone else but no answer given, please HELP!

Thanks

 

[cdhotfire]

For #3, I am assuming asteroid is at rest. So
Hero
$m_{H}= m$
$v_{iH}= 0 m/s$
Asteroid
$m_{A}= 1000m$
$v_{iA}= 0 m/s$
$v_{fA}= 100 m/s$
So momentum before = momentum after
$0 = m_{A}v_{fA} + m_{H}v_{fH}$

 

[wais]

for reaching out for help with these momentum questions! Here are the answers to each of the questions:

1. When the astronauts begin tossing the balls simultaneously, each ball will have an initial velocity of zero due to the lack of gravity. As the balls are tossed back and forth between the astronauts, they will continue to gain momentum and increase in speed. This is because momentum is conserved in a closed system, and the only external force acting on the balls is the force from the astronauts tossing them. Eventually, the balls will form a circular motion around the astronauts as they continue to toss them to one another.

2. After the larger fish swallows the smaller fish, the total mass of the system will be 6 kg. Using the law of conservation of momentum, we can calculate the speed of the larger fish after lunch:

m1v1 + m2v2 = (m1 + m2)v

(5 kg)(1 m/s) + (1 kg)(0 m/s) = (6 kg)(v)

5 kgm/s = 6 kgv

v = 5/6 m/s

If the smaller fish were swimming towards the larger fish at 4 m/s, we can use the same equation to calculate the speed of the larger fish after lunch:

m1v1 + m2v2 = (m1 + m2)v

(5 kg)(1 m/s) + (1 kg)(-4 m/s) = (6 kg)(v)

5 kgm/s - 4 kgm/s = 6 kgv

1 kgm/s = 6 kgv

v = 1/6 m/s

3. According to the law of conservation of momentum, the total momentum of the system before and after the asteroid is hurled by Superman must be equal. We can set up the following equation:

m1v1 = m2v2

Where m1 is the mass of Superman and m2 is the mass of the asteroid. We are given that the asteroid is 1000 times more massive than Superman, so we can substitute 1000m1 for m2:

m1v1 = (1000m1)v2

We are also given that the asteroid is hurled at 100 m/s, so we can set v1 to 100 m/s:

(100 m/s)m1 = (1000m1)v2

Solving for v2, we get:

v