An apartment has the dimensions 18 m by 9 m by 6 m. The temperature is 25°C, and the relative humidity is 59 percent. What is the total mass (in kg) of water vapor in the air in the apartment?

(a) The work done by the donkey on the cart is 59,721.9 J.

(b) The work done by the force of gravity on the cart is -48,434.87 J.

(c) The work done on the cart by friction during this time is 11,315.12 J.

(a) The work done by the donkey on the cart is calculated as follows;

Wd = Fd cosθ

where;

Wd = 375 N x 163 m x cos(12.3)

Wd = 59,721.9 J

(b) The work done by the force of gravity on the cart is calculated as;

Wg =  Fg x d x cosθ

Where;

θ = 90⁰ + 4.03⁰ = 94.03⁰

Wg = (431 kg x 9.81 m/s²) x 163 m x cos (94.03)

Wg = -48,434.87 J

(c) The work done on the cart by friction during this time is calculated as;

Wf = Ff x d x cosθ

where;

Ff = μmg cosθ

Ff = 0.0165 x 431 kg x 9.81 x cos (4.03)

Ff = 69.59 N

Wf = 69.59 x 163 x cos (4.03)

Wf = 11,315.12 J

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Sarah’s velocity immediately after the collision is 4.3 m/s west.

option C is the correct answer.

Sarah’s velocity immediately after the collision is calculated by applying the principle of conservation of linear momentum as follows;

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

where;

Sarah’s velocity immediately after the collision is calculated as;

179 (1.6) + 163(3.9) = 179v₁ + 163(0.9)

922.1 = 179v₁ + 146.7

179v₁ = 775.4

v₁ = 4.3 m/s

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Graphs can help to demonstrate the qualitative relationship between a set of data by identifying patterns among these data.

Graphs can allow readers to identify a lot of information among a set of data. The most common information to be evaluated through the graphs is the existence of patterns between the data.

For example, a line graph can show the change in a variable over time, allowing readers to see if there is a consistent increase or decrease.

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If a wave has an amplitude of 0.0800 m and is moving 7.33 m/s. The

wavelength of the wave is 1.69m.

The wavelength of a wave can be determined using the equation:

Wavelength = velocity / frequency

To determine the frequency we need to calculate the reciprocal of the time it takes for one complete oscillation.

frequency = 1 / time

frequency = 1 / 0.230

frequency ≈ 4.35 Hz

Substitute the values into the wavelength equation:

wavelength = velocity / frequency

wavelength = 7.33 / 4.35

wavelength ≈ 1.69m

Therefore the wavelength of the wave is approximately 1.69 meters.

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The following elements are matched with their number of neutrons

1. 88 38 Sr - b. 50

2. 39 19 Ka - a. 20

3. 14 6 Carbon - c. 8

4. 234 90 Thorium plus 4 2 Helium - d. 74

To determine the number of neutrons for each element, we need to subtract the atomic number (which represents the number of protons) from the mass number (which represents the total number of protons and neutrons).

1. 88 38 Sr:

The atomic number of strontium (Sr) is 38, which means it has 38 protons. The mass number is 88. Subtracting the atomic number from the mass number: 88 - 38 = 50. Therefore, the number of neutrons in strontium is 50.

2. 39 19 Ka:

The atomic number of potassium (K) is 19, indicating 19 protons. The mass number is 39. Subtracting the atomic number from the mass number: 39 - 19 = 20. Hence, the number of neutrons in potassium is 20.

3. 14 6 Carbon:

The atomic number of carbon (C) is 6, representing 6 protons. The mass number is 14. Subtracting the atomic number from the mass number: 14 - 6 = 8. Thus, the number of neutrons in carbon is 8.

4. 234 90 Thorium plus 4 2 Helium:

The atomic number of thorium (Th) is 90, which means it has 90 protons. The mass number is 234. Subtracting the atomic number from the mass number: 234 - 90 = 144. However, there is also an additional helium (He) isotope mentioned with a mass number of 4 and atomic number of 2. Adding the number of neutrons from thorium and helium: 144 + 2 = 146. Hence, the number of neutrons in thorium plus helium is 146.

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The reactive force when a fish swims through water is the force of the water on the fish. This is an example of Newton’s third law of motion which states that for every action, there is an equal and opposite reaction. The active force is the fish pushing against the water, so the reactive force would be the reverse, the equal force of the water pushing back on the fish.

The total distance is 105 kilometers and the total displacement is 15 kilometers east. Option C

To calculate the total distance, we add the distances traveled in each leg of the journey: 60 kilometers (from A to B) + 45 kilometers (from B back to A) = 105 kilometers.

However, displacement refers to the change in position of an object in a straight line from its starting point to its ending point. In this case, since the boat starts and ends at the same point (A), the total displacement is zero.

Hence The total distance is 105 kilometers and the total displacement is 15 kilometers east.

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The crate moves this time because the applied force of 150 N is greater than the maximum static friction force that opposes the motion of the crate. Static friction is a force that opposes the relative motion between two objects in contact. The maximum static friction force is determined by the normal force and the coefficient of static friction between the two surfaces in contact. The harder the surfaces are pushed together, the more force is needed to move them. When the applied force exceeds the maximum static friction force, the crate will start to move. Once in motion, it is easier to keep it in motion than it was to get it started because the kinetic friction force is less than the static friction force.

The kinetic energy of the book after it is slids a distance of 2 meters will be 10 Joules.

The work-energy theorem states that "the work done on an object is the change in its kinetic energy".

Hence;

Kinetic energy = work done

Note that: work-done is expressed as:

Work done = f × d

Where f is force applied and d is distance traveled.

Given that:

Force applied f = 5 newton

Distance d = 2 meters

Work done = ?

Plug these values into the above formula and solve for the workdone.

Work done = f × d

Work done = 5N × 2m

Work done = 10Nm

Work done = 10 Joules

Therefore, the kinetic energy is 10 Joules.

Option B) 10 J is the correct answer.

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The distance covered by a ball in the first second of free fall is approximately 4.9 meters.

When an object falls freely under the influence of gravity, it experiences constant acceleration. In the case of Earth's gravity, the acceleration due to gravity is approximately 9.8 m/s². This means that the velocity of the falling object increases by 9.8 meters per second every second.

To determine the distance covered by the ball in the first second, we can use the equations of motion for uniformly accelerated motion.

The equation that relates distance (d), initial velocity (u), acceleration (a), and time (t) is:

d = ut + (1/2)at²

In this case, the initial velocity is zero (as the ball starts from rest), the acceleration is 9.8 m/s², and we want to find the distance covered in the first second (t = 1 second).

Plugging in the values:

d = 0 * 1 + (1/2) * 9.8 * (1)^2

d = 0 + (1/2) * 9.8

d = 0 + 4.9

d = 4.9 meters

Therefore, the ball covers a distance of approximately 4.9 meters in the first second of free fall.

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The reaction equations for the steps involved in the decay of U-238 to Ra-226 are;

[tex]^{238}_{92}U\ \rightarrow \ ^{234}_{90}Th \ + \ ^{4}_{2}He[/tex]

[tex]^{234}_{90}Th \ \rightarrow \ ^{230}_{88}Ra \ + \ ^{4}_{2}He[/tex]

[tex]^{230}_{88}Ra \ \rightarrow \ ^{226}_{86}Ra \ + \ ^{4}_{2}He[/tex]

The radioactive equation for the decay of U-238 to Ra-226 is calculated as follows;

First the uranium atom (U-238) will decay thorium by emitting alpha particle as shown in the equation below;

[tex]^{238}_{92}U\ \rightarrow \ ^{234}_{90}Th \ + \ ^{4}_{2}He[/tex]

The second stage is, the thorium will decay to radium by emitting alpha particles again as shown below;

[tex]^{234}_{90}Th \ \rightarrow \ ^{230}_{88}Ra \ + \ ^{4}_{2}He[/tex]

The third, and final stage, the radium will decay to an isotope of radium again, by emitting alpha particle as shown below;

[tex]^{230}_{88}Ra \ \rightarrow \ ^{226}_{86}Ra \ + \ ^{4}_{2}He[/tex]

Thus, the reaction equations for the steps involved in the decay of U-238 to Ra-226 are;

[tex]^{238}_{92}U\ \rightarrow \ ^{234}_{90}Th \ + \ ^{4}_{2}He[/tex]

[tex]^{234}_{90}Th \ \rightarrow \ ^{230}_{88}Ra \ + \ ^{4}_{2}He[/tex]

[tex]^{230}_{88}Ra \ \rightarrow \ ^{226}_{86}Ra \ + \ ^{4}_{2}He[/tex]

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There are 630,720,000 seconds in 20 years.

To calculate the number of seconds in 20 years, we need to consider the number of seconds in a minute, minutes in an hour, hours in a day, and days in a year.

1 minute consists of 60 seconds.

1 hour contains 60 minutes (60 minutes × 60 seconds = 3600 seconds).

1 day consists of 24 hours (24 hours × 3600 seconds = 86,400 seconds).

1 year typically consists of 365 days (365 days × 86,400 seconds = 31,536,000 seconds).

To find the number of seconds in 20 years, we multiply the number of seconds in one year by 20:

20 years × 31,536,000 seconds = 630,720,000 seconds.

Therefore, there are 630,720,000 seconds in 20 years.

This calculation assumes a non-leap year with 365 days.

If the 20 years span a leap year, the total number of seconds would be slightly higher, accounting for the extra day in the leap year.

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