A football (450 g) falls vertically from rest onto the ground from a height of 5.0 m. If the force that

An astronaut goes out for a space walk. Her mass (including space suit, oxygen tank, etc.) is 100 kg. Suddenly, disaster strikes

Marina CMI [18]

Answer:

Part A:

Unknown variables:

velocity of the astronaut after throwing the tank.

maximum distance the astronaut can be away from the spacecraft to make it back before she runs out of oxygen.

Known variables:

velocity and mass of the tank.

mass of the astronaut after and before throwing the tank.

maximum time it can take the astronaut to return to the spacecraft.

Part B:

To obtain the velocity of the astronaut we use this equation:

-(momentum of the oxygen tank) = momentum of the astronaut

-mt · vt = ma · vt

Where:

mt = mass of the tank

vt = velocity of the tank

ma = mass of the astronaut

va = velocity of the astronaut

To obtain the maximum distance the astronaut can be away from the spacecraft we use this equation:

x = x0 + v · t

Where:

x = position of the astronaut at time t.

x0 = initial position.

v = velocity.

t = time.

Part C:

The maximum distance the astronaut can be away from the spacecraft is 162 m.

Explanation:

Hi there!

Due to conservation of momentum, the momentum of the oxygen tank when it is thrown away must be equal to the momentum of the astronaut but in opposite direction. In other words, the momentum of the system astronaut-oxygen tank is the same before and after throwing the tank.

The momentum of the system before throwing the tank is zero because the astronaut is at rest:

Initial momentum = m · v

Where m is the mass of the astronaut plus the equipment (100 kg) and v is its velocity (0 m/s).

Then:

initial momentum = 0

After throwing the tank, the momentum of the system is the sum of the momentums of the astronaut plus the momentum of the tank.

final momentum = mt · vt + ma · va

Where:

mt = mass of the tank

vt = velocity of the tank

ma = mass of the astronaut

va = velocity of the astronaut

Since the initial momentum is equal to final momentum:

initial momentum = final momentum

0 = mt · vt + ma · va

- mt · vt = ma · va

Now, we have proved that the momentum of the tank must be equal to the momentum of the astronaut but in opposite direction.

Solving that equation for the velocity of the astronaut (va):

- (mt · vt)/ma = va

mt = 15 kg

vt = 10 m/s

ma = 100 kg - 15 kg = 85 kg

-(15 kg · 10 m/s)/ 85 kg = -1.8 m/s

The velocity of the astronaut is 1.8 m/s in direction to the spacecraft.

Let´s place the origin of the frame of reference at the spacecraft. The equation of position for an object moving in a straight line at constant velocity is the following:

x = x0 + v · t

where:

x = position of the object at time t.

x0 = initial position.

v = velocity.

t = time.

Initially, the astronaut is at a distance x away from the spacecraft so that

the initial position of the astronaut, x0, is equal to x.

Since the origin of the frame of reference is located at the spacecraft, the position of the spacecraft will be 0 m.

The velocity of the astronaut is directed towards the spacecraft (the origin of the frame of reference), then, v = -1.8 m/s

The maximum time it can take the astronaut to reach the position of the spacecraft is 1.5 min = 90 s.

Then:

x = x0 + v · t

0 m = x - 1.8 m/s · 90 s

Solving for x:

1.8 m/s · 90 s = x

x = 162 m

The maximum distance the astronaut can be away from the spacecraft is 162 m.

6 0

3 years ago

I need your opinion on this

DiKsa [7]

Block that fool, move on, take a nice warm bath, but on some music and vibe dawg, it might be hard to get over something like this, but just know that person was in the wrong the whole time.

5 0

3 years ago

A ruby laser delivers a 16.0-ns pulse of 4.20-MW average power. If the photons have a wavelength of 694.3 nm, how many are conta

stepan [7]

Answer:

The value is $n = 2.347 *10^{17} \ photons$

Explanation:

From the question we are told that

The amount of power delivered is $P = 4.20 \ M W = 4.20 *10^{6} \ W$

The time taken is $t = 16.0ns = 16.0 *10^{-9} \ s$

The wavelength is $\lambda = 694.3 \ nm = 694.3 *10^{-9} \ m$

Generally the energy delivered is mathematically represented as

$E = P * t = \frac{n * h * c }{\lambda }$

Where $h$ is the Planck's constant with value $h = 6.262 *10^{-34} \ J \cdot s$

c is the speed of light with value $c = 3.0*10^{8} \ m/s$

So

$4.20 *10^{6} * 16*10^{-9}= \frac{n * 6.626 *10^{-34} * 3.0*10^{8} }{694.3 *10^{-9}}$

=> $n = 2.347 *10^{17} \ photons$

4 0

3 years ago

Which statements about a neutral atom are correct? Select all that apply. (1) A neutral atom is composed of both positively and

Bad White [126]

Answer:

(3) The electrons are attracted to the positively charged nucleus.

(4) Positively charged protons are located in the tiny, massive nucleus.

(6) The negatively charged electrons are spread out in a "cloud" around the nucleus.

Explanation:

An atom is the basic particle in which a matter is formed. It can either be charged or neutral. When it losses or gains an extra electron, it becomes charged, an ion. While a neutral atom is an atom which has no charge, because it has the same number of electrons and protons. The protons are located in the tiny massive nucleus of the atom, while the electrons are in orbits or cloud around the nucleus.

7 0

3 years ago

At some airports there are speed ramps to help passengers get from one place to another. A speed ramp is a moving conveyor belt

Harrizon [31]

Answer:

It will take you 30.8 s to travel the 120 m of the ramp.

Explanation:

Hi there!

The equation for the position of an object moving in a straight line is:

x = x0 + v * t

Where:

x = position at time t

x0 = initial position

v = velocity

t = time

In this case, we will consider the start of the ramp as the origin of our reference system so that x0 = 0.

Now, let´s calculate the speed of the person walking on the ground:

x = v * t

120 m = v * 72 s

v = 120 m / 72 s

v = 1.7 m/s

If you walk on the ramp with that speed, your total speed will be your walking speed plus the speed of the ramp because both are in the same direction. Then, using the equation for the position:

x = v * t

In this case, v = speed of the ramp + walking speed

v = 2.2 m/s + 1.7 m/s = 3.9 m/s

120 m = 3.9 m/s * t

t = 120 m / 3.9 m/s = 30.8 s

It will take you 30.8 s to travel the 120 m

8 0

3 years ago