2. A nutty professor leaves a history classroom and walks 10. meters north to a drinking fountain. Then, in a daze, she turns and walks 30. meters south to an art classroom. (draw vectors to scale to show your work)
(a) What is the professor’s total displacement from the classroom to the art classroom?
(b) What was the total distance she traveled?

Answer:

Train A has a speed 20 miles per hour greater than that of train B. If train A travels 300 miles in the same times train B travels 220 miles, what are the speeds of the two trains?

2. A woman has a total of $13,000 to invest. She invests part of the money in an account that pays 11% per year and the rest in an account that pays 12% per year. If the interest earned in the first year is $1490 how much did she invest in each account?

Explanation:

This question involves the concepts of the law of conservation of momentum and velocity.

The velocity of the eight ball is "5.7 m/s".

According to the law of conservation of momentum:

[tex]m_1u_1+m_2u_2=m_1v_1+m_2v_2[/tex]

where,

m₁ = mass of number three ball = 5 g

m₂ = mass of the eight ball = 6 g

u₁ = velocity of the number three ball = 3 m/s

u₂ = velocity of the eight ball = - 1 m/s (negative sign due to opposite direction)

v₁ = final velocity of the three number ball = - 5 m/s

v₂ = final velocity of the eight ball = ?

Therefore,

(5 g)(3 m/s) + (6 g)(- 1 m/s) = (5 g)(- 5 m/s) + (6 g)(v₂)

[tex]v_2=\frac{34\ g.m/s}{6\ g}\\\\[/tex]

v₂ = 5.7 m/s

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Both carts experience the same force but Cart A has a greater speed after the recoil.

The given parameters;

Apply the principle of conservation of linear momentum to determine the velocity of the carts after collision;

[tex]m_Av_0_A\ + m_Bv_0_B = m_Av_f_A \ + m_Bv_f_B\\\\the \ initial \ velocity \ of \ both \ carts = 0\\\\0.4(0) + 0.8(0) = 0.4v_f_A + 0.8v_f_B\\\\0 = 0.4v_f_A + 0.8v_f_B\\\\0.4v_f_A = -0.8v_f_B\\\\v_f_A= \frac{-0.8 v_f_B}{0.4} \\\\v_f_A = - 2 \ v_f_B \ \ m/s[/tex]

According to Newton's third law of motion, action and reaction are equal and opposite. The force exerted on cart A is equal to the force exerted on cart B but in opposite direction.

[tex]F_A = -F_B[/tex]

Thus, the correct statement that compares the motion and forces acting on the two carts is "Both carts experience the same force but Cart A has a greater speed after the recoil."

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Hi there!

[tex]\large\boxed{\text{Angular acceleration.}}[/tex]

For a rigid body rotating about a fixed axis, its angular characteristics ⇒ angular acceleration and velocity are constant throughout.

However, its LINEAR velocities/accelerations differ because of the following relationships:

v = ωr

a = αr

Thus, a point closer to the axis of rotation has a smaller linear velocity or acceleration compared to a point along the edge.

Answer:

"electric or magnetic"

F = q E    force on charge q due to electric field E

F = q v x B       force on charge q due to magnetic field B

Answer:

The Agricultural Revolution of the 18th century paved the way for the Industrial Revolution in Britain. New farming techniques and improved livestock breeding led to amplified food production. This allowed a spike in population and increased health. The new farming techniques also led to an enclosure movement

Answer:

2 miles

Explanation:

Answer:

hi there !

1 hour -------> 620 miles

3 1/2 ---------> ?

the number of miles the airplane travels in 3 1/2 hours

= 3 1/2 × 620 = "2170" miles

The force might make the object move or bring the object to rest or change in direction of motion

[tex]\\ \sf\Rrightarrow F_{net}=F_1+F_2+F_3+F_4[/tex]

[tex]\\ \sf\Rrightarrow F_{net}=20N+20N+10N-10N[/tex]

[tex]\\ \sf\Rrightarrow F_{net}=40N[/tex]

Answer:

E.visible lights

Explanation:

hope its attachments

Considering the ideal gas law, 116.06 moles of are needed to fill a 2000 L weather balloon at 210 K and 1 atm pressure.

An ideal gas is a theoretical gas that is considered to be composed of randomly moving point particles that do not interact with each other. Gases in general are ideal when they are at high temperatures and low pressures.

The pressure, P, the temperature, T, and the volume, V, of an ideal gas, are related by a simple formula called the ideal gas law:  

P×V = n×R×T

where P is the gas pressure, V is the volume that occupies, T is its temperature, R is the ideal gas constant, and n is the number of moles of the gas. The universal constant of ideal gases R has the same value for all gaseous substances.

In this case, you know:

Replacing in the ideal gas law:

1 atm× 2000 L = n× 0.082057 [tex]\frac{atmL}{molK}[/tex]× 210 K

Solving:

[tex]n=\frac{1 atmx 2000 L}{0.082057 \frac{atmL}{molK}x 210 K}[/tex]

n=116.06 moles

Finally, 116.06 moles of are needed to fill a 2000 L weather balloon at 210 K and 1 atm pressure.

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[tex]\\ \sf\longmapsto s=ut+\dfrac{1}{2}at^2[/tex]

[tex]\\ \sf\longmapsto s=5.5(10)+\dfrac{1}{2}(8)(5.5)^2[/tex]

[tex]\\ \sf\longmapsto s=55+4(5.5)^2[/tex]

[tex]\\ \sf\longmapsto s=55+4(30.25)[/tex]

[tex]\\ \sf\longmapsto s=55+121[/tex]

[tex]\\ \sf\longmapsto s=176m[/tex]

The kinetic energy of a toy truck with a mass of 0. 75 kg and a velocity of 4m/s is 6J.

HOW TO CALCULATE KINETIC ENERGY:

The kinetic energy of a moving body can be calculated by using the following formula:

K.E = ½mv²

Where;

According to this question, a toy truck has a mass of 0.75 kg and a velocity of 4 m/s. The kinetic energy is calculated as follows:

K.E = ½ × 0.75 × 4²

K.E = 8 × 0.75

K.E = 6J

Therefore, the kinetic energy of a toy truck with a mass of 0. 75 kg and a velocity of 4m/s is 6J.

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Answer:

because of the gravity of the earth

Answer:

Homogenous Mixture

Explanation:

The composition in paint is uniform so every part of it looks the same throughout the paint.

Thermal expansion is the tendency of matter to change its shape dimensions, density in response to a change in temperature.

  2. Gases

    3. Liquids

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The change of velocity is from 18.5 to 46.1 m/s or 46.1 - 18.5 = 27.6 m/s. The time of change is 2.47 s. So the acceleration is 27.6 m/s / 2.47 s = 11.17 m/s^2. The distance traveled is average velocity times time of travel.

Answer:

This above a triangle that models our situation.

Explanation:

We have a two componens., since we have a western componet and southern component. One travel in a southern direction. and the other travel in the west.

Let the component that travel in the south be the length of a.

According to the problem, the westard component is half of that so let that length be a/2.

Now we must find the angle of the wind in the South.

This means that what is angle that is opposite of the western componet because that angle is the most southward angle. So know we apply the tan property.

[tex] \tan(x) = \frac{opp}{adj} [/tex]

Our side opposite of the angle we trying to find is the western component and the side adjacent to it is the southern component. Also remeber since western and Southern negative displacements, we have

[tex] \tan(x) = \frac{ - \frac{a}{2} }{ - a} [/tex]

[tex] \tan(x) = - \frac{a}{2} \times - \frac{1}{a} = \frac{1}{2} [/tex]

Now we take the arctan or inverse tan of 1/2.

[tex] \tan {}^{ - 1} ( \frac{1}{2} ) = 26.57[/tex]

Based on the information about vector components and graph provided, the angle of the wind with the south is 26.57°.

The western and southern component have a negative displacement as shown in the graph.

Let the southern component be -x

The western component is half of -x = -x/2

Since the angle is with the south, the trigonometric ratio to be used to find the angle is:

Tan θ = -×/2 /-x

Tan θ = 1/2

θ = tan^-1(0.5)

θ = 26.6°

Therefore, angle of the wind with the south is 26.57°.

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Answer:

1 N

Explanation:

1) You'll just have to sum the force vectors, and since they are opposite, you'll calculate the difference of their magnitudes, in absolute value.

Ftot = |F1 - F2| = 6N - 5N = 1N

2)The direction will be the same as the greater force's direction.

Answer:

20 ft/sec / 32 ft/sec^2 = .625     to reach top

2 * .625 = 1.25

It will be on the ground at t = 0 and t = 1.25

You can also solve the equation:

H = 0 = V0 t - 1/2 g t^2

Obviously, at t=0 h = 0

V0 = 1/2 g t    is a solution

t = 20 * 2 / 32 = 1.25 sec

The location of the point F that partitions a line segment from D to E ([tex]\overline{DE}[/tex]), that goes from negative 4 to positive 5, into a 5:6 ratio is fifteen halves (option 4).  

We need to calculate the segment of the line DE to find the location of point F.

Since point D is located at negative -4 and point E is at positive 5, we have:

[tex] \overline{DE} = E - D = 5 - (-4) = 9 [/tex]

Hence, the segment of the line DE ([tex]\overline{DE}[/tex]) is 9.

Knowing that point F partitions the line segment from D to E ([tex]\overline{DE}[/tex]) into a 5:6 ratio, its location would be:

[tex] F = \frac{5}{6}\overline{DE} = \frac{5}{6}9 = 5*\frac{3}{2} = \frac{15}{2} [/tex]  

Therefore, the location of point F is fifteen halves (option 4).

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I hope it helps you!

Answer:

The above answer is actually incorrect - the real answer is B. 1/11

Explanation:

I'm adding a ss below for proof

Hope this helped!

I'd really appreciate Brainliest :)

Answer:

Since there is no external force, there is no change (movement) in the center of mass. Internally, the center of mass might change position, but the external result is still zero net velocity.

The net recoil velocity must be zero.

Answer:

Before collision:

momentum to right = .14 * 3.5 = .49 kg m / s

momentum to left = .62 * 4.81 = 2.98 kg m / s

Total momentum = .49 - 2.98 = - 2.49 to left

M V = -2.49    net momentum to left

V = -2.49 / (.14 + .62) = -3.28 m/s to left

Answer:

-4,200,000 J

Explanation:

The horizontal component of the velocity is equal to: D. 15 m/s.

Given the following data:

To determine the horizontal component of the velocity:

The horizontal component of the velocity represents the influence of velocity  in displacing an object or projectile in the horizontal direction.

Mathematically, the horizontal component of velocity is given by the formula:

[tex]V_x = Vcos(\theta)[/tex]

Substituting the given parameters into the formula, we have;

[tex]\\\\V_x = 30cos(60)\\\\V_x = 30 \times 0.5[/tex]

Horizontal component, Vx = 15 m/s

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