A pilot flies her route in two straight-line segments. The displacement vector A for the first segment has a magnitude of 232 km and a direction 30.0o north of east. The displacement vector B for the second segment has a magnitude of 168 km and a direction due west. The resultant displacement vector is R = A + B and makes an angle θ with the direction due east. Using the component method, find (a) the magnitude of R and (b) the directional angle θ.

Answer:

(i) The period, T is 0.25 s

(ii) The angular velocity, ω is 25.136 rad/s

(iii) The linear velocity is, v is 50.27 m/s

Explanation:

Given;

number of revolution of the particle, N = 240 revolutions per minutes

radius of the circle, R = 2m

(i) The period is given by;

[tex]T = \frac{2\pi}{\omega}[/tex]

where;

ω is angular velocity  

[tex]\omega = (240 \frac{rev}{min}) *(\frac{1 \ min}{60 \ s} )*(2\pi \frac{rad}{rev})\\\\ \omega = 25.136 \ rad/s[/tex]

[tex]T = \frac{2\pi }{\omega}\\\\ T = \frac{2\pi}{25.136}\\\\T = 0.25 \ s[/tex]

(ii) angular velocity, ω  = 25.136 rad/s

(iii) linear velocity is given by;

v = ωR

v = (25.136 rad/s) x (2 m)

v = 50.27 m/s

Answer:

[tex]Speed = 87 km/h[/tex]

Explanation:

Given

Total Distance = 720km

Average Speed = 90km/h

Average Speed (285km) = 95km/h

Required

Determine the average speed for the rest of the journey

First we need to determine the time taken to complete the journey using

[tex]Speed = \frac{Distance}{Time}[/tex]

[tex]90 = \frac{720}{Time_1}[/tex]

Make Time the subject of formula

[tex]Time_1 = \frac{720}{90}[/tex]

[tex]Time_1 = 8 hour[/tex]

Next, we determine the time taken to complete 285km of the journey using

[tex]Speed = \frac{Distance}{Time}[/tex]

[tex]95 = \frac{285}{Time_2}[/tex]

Make Time the subject of formula

[tex]Time_2 = \frac{285}{95}[/tex]

[tex]Time_2 = 3 hours[/tex]

The difference between these calculated times is the time taken to complete the rest of the journey

[tex]Time = Time_1 - Time_2[/tex]

[tex]Time = 8\ hour - 3\ hour[/tex]

[tex]Time = 5\ hour[/tex]

Also, we need to calculate the distance of the rest of the journey

[tex]Distance = 720\ km - 285\ km[/tex]

[tex]Distance = 435\ km[/tex]

The average speed can then be calculated;

[tex]Speed = \frac{Distance}{Time}[/tex]

[tex]Speed = \frac{435}{5}[/tex]

[tex]Speed = 87 km/h[/tex]

Hence, the average speed of the rest of the journey is 87km/h

Answer:

2. it has an acceleration directed toward the center of its path

Explanation:

For a car moving with constant velocity around a circular track, there is a a change in the direction of the velocity at every point on the path taken by the car around the track. This change in direction generates an acceleration on the car which will be directed towards the center of the track. This is why the inertia force on a person inside the car when it is driven around a circular track is usually away from the center of the track, since the inertia force acts in an opposite direction to the acceleration on a body.

Answer:

A diet high in fat, calories, and cholesterol increases your risk of diabetes. A poor diet can lead to obesity (another risk factor for diabetes) and other health problems. A healthy diet is high in fiber and low in fat, cholesterol, salt, and sugar. Also, remember to watch your portion size.

Answer: you would feel more gravity

Explanation: the more mass of an object the more pull

Answer:

112.5 lb/ft³

405.93 kg/m³

0.406

Explanation:

given that

Weight of the container, w(c) = 450 lb

Volume of fluid, v(f) = 4 ft³

Weight of empty container, w(e) = 50 lb

Specific weight is said to be the weight per unit volume. Thus, the specific weight of this fluid is

w(s) = 450 / 4

w(s) = 112.5 lb/ft³

Mass density is the ratio of the mass of the fluid, with respect to the volume.

ρ = m/v

Since the question gives us the mass in weight, we'd have to convert it to mass from weight.

mass = weight / acceleration due to gravity

mass = 450 / 9.81

mass = 45.87 kg

Also, since the mass is going to be in kg, the volume also has to be in m³, thus needing a conversion.

4 ft³ = 0.113 m³

Mass density = 45.87 / 0.113

Mass density = 405.93 kg/m³

Specific gravity of the fluid is simply given as mass density / 1000. Therefore,

g(s) = 405.93 / 1000

g(s) = 0.406

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Answer:

c

Explanation:

energy isn't stored and it doesn't change to mass

The ball has some kinetic energy when it hits the floor, but some of it is changed, so it loses some of it each time it bounces. After a few bounces, the ball has so little kinetic energy remaining that it stops bouncing. Thus, option C is correct.

Since the gravitational potential energy, which can be transformed back into kinetic energy on the rebound, increases with the drop height, the consequent bounce height will likewise rise.

Because it has the most elasticity, the rubber ball will rebound the highest when all three balls are dropped from the same height. Because rubber is incredibly elastic, it squishes or compresses as it touches the ground but immediately snaps back to its original shape.

Therefore, Additionally, some energy is changed into other forms like heat and sound. The majority of these additional energy sources are lost and not recovered, causing the ball to bounce back to a lesser height.

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Answer:

Explanation:

A. Q= It

30E-3A=q

Ne = q

30E-3/1.6*10-19= N

N= 1.8*10^16 electrons

B. Power= I x v

= 30*10^-3A x 100*10^3v

= 3000watts

Answer:

16.80672269 m/s

Explanation:

100 divide by 5.95 seconds

Answer:

16.8m/s

Explanation:

S=D/T

=

[tex] \frac{100}{5.95} [/tex]

=16.80672269

=16.8

Answer:

   h ’= 0.6963 m

this is the height of the part of the post it supports.

Explanation:

For this exercise we can use the trigonometric relationships

Let's start by finding the vertical component of the height of the pole

             cos 30 = x / L

             x = L cos 30

             x = 6 cps 30

             x = 5.196 m

with this length, the post has the same height as the building, so there are

               Aₓ = L -x

               Δx = 6 -5.196

               Δx = 0.804 ft

the height of this section is

               cos 30 = h ’/ Dx

               h ’= 0.804 cos30

               h ’= 0.6963 m

this is the height of the part of the post it supports.

The question is missing the alternatives. Here is the complete question.

Two vectors of magnitude |A| = 8units and |B| = 5units make an angle that can vary from 0° to 180°. The magnitude of the resultant vector A+B CANNOT have the value of:

A. 2 units

B. 5 units

C. 8 units

D. 12 units

Answer: A. 2 units

Explanation: Vector is an entity that has characteristics as magnitude and direction. Resultant vector is the "sum" of 2 or more vectors.

In this question, the vectors have magnitude and angle varies from 0° to 180°.

When angle between vectors A and B is 0°, they are parallel and pointing to the same direction, so:

[tex]V_{R} = |A| + |B|[/tex]

[tex]V_{R}=8+5[/tex]

[tex]V_{R}[/tex] = 13

When the angle is 180°, it means vectors are in opposing directions, so:

[tex]V_{R} = |A| - |B|[/tex]

[tex]V_{R} = 8-5[/tex]

[tex]V_{R}[/tex] = 3

From the calculations, we can conclude the magnitude of resultant vector varies between 3 and 13.

The least value is 3, so it cannot have a value of 2 units.

Distance = (speed) x (time)

Distance = (3.75 m/s) x (5.0 s)

Distance = 18.75 meters

Answer: 3.75 x 5.0= 18.75 meters

Explanation:

Answer:

Bolt

Explanation:

Answer:

x₂ = 0.01336

Explanation:

In this exercise we use the translational equilibrium equation

          F₁₃ - F₂₃ = 0

          F₁₃ = F₂₃

at the point where charge 3 is placed the two electric forces have the same magnitude

let us use the expression of Coulomb's law for the electric force

         F₁₃ = ka q₁ q₃ / r₁₃²

         F₂₃ = ka q₂ q₃ / r₂₃²

we substitute

         k q₁ q₃ / r₁₃² = k q₂ q₃ / r₂₃²

now imprescriptibility suppose that particle 1 is at the origin of the coordinate system, particle 2 is at a distance d = 2.00cm = 2 10-2 m, therefore let's call the distance from particle 1 to particle 3 as x

            r₁₃ = x

            R₂₃ = d-x

In the exercise we are given the charges for the particle1 q1 = q, for the particle 2 the charge is q2 = 4q the distance between them is d = 2.00cm = 0.0200 m, the value of q = 2.00 nC = 2.00 10⁻⁹ C

let's substitute these values

              q₁ / x₂ = q₂ / (d-x)²

let's clear x

              (d-x)² = q₂ / q₁    x²

              d² - 2dx + x₂ = q₂ /q₁   x²

               x² (1-q₂ / q₁) - 2d x + d² = 0

let's substitute the values ​​and solve the quadratic equation

              x² (1 - 4q / q) - 2 0.02 x + 0.02² = 0

              -3 x² - 0.04 x + 0.0004 = 0

                x² + 0.0133 x - 0.0001333 = 0

               x = [-0.0133 ±√(0.0133² + 4 0.00013333)] / 2

                x = [-0.0133 + - 0.026664] /2

              x₁ = -0.01998 m

              x₂ = 0.01336 m

Since load 3 must be between charged 1 and 2 the correct answer is

x₂ = 0.01336

Answer:

4

Explanation:

friction

weight

normal reaction

force to overcome inertia

Answer:

1

Explanation:

--->

Answer:

The value  is  [tex]h =  52.2 \  m[/tex]

Explanation:

From the question we are told that

 The  velocity  at which he hit the water  is  [tex]v  =  32 \  m/s[/tex]

Generally from kinematic equation

     [tex]v^2 =  u^2  + 2gh[/tex]

Here the initial velocity u = 0 m/   given that the gannet started the jump from rest.

  =>   [tex]32^2  =  0^2  +  2*(9.8)h[/tex]

 =>     [tex]h =  52.2 \  m[/tex]

Answer:

the answer to this question would be cut the exercise portion down (D)

this is because warm ups and cooling down during exercise are more important than the exercise itself

Explanation:

Answer:

F = 6.25 N

Explanation:

Given that,

Mass of the book is 1.25 kg

Acceleration of the book is 5 m/s²

We need to find the net force needed to accelerate the book. Net force is given by :

F = ma

[tex]F=1.25\times 5\\\\F=6.25\ N[/tex]

So, 6.25 N of force is acting on the book.

Answer:

The ping pong ball is hollow.

Explanation:

Since a ping pong ball, unlike the golf ball, is only filled with air, it is less dense. Air is notably LESS dense than solids, which is what comprises the inside of a golf ball.

Answer:

18.4615385 amps

Explanation:

The voltage V in volts (V) is equal to the current I in amps (A) times the resistance R in ohms (Ω):

Answer:

Trevor's taxi would cause higher levels of air pollution

Explanation:

Trevor's taxi use diesel oil.

Diesel is less cleaner than LPG.

Compared to automotive pollution from petrol and diesel, pollutants from LPG-driven cars include lower amounts of petroleum hydrocarbons, nitrogen oxides , sulphur oxides, ozone contamination and particulate matter.

Answer:

6.416*10^ 8C

Explanation:

First we find mass of the water

Mass= density x volume

=1.2*1000= 1200g

To find number of moles we use

N= mass/ molar mass

= 1200/18.02= 66.6mol

So the total number of water molecules is

66.6* 6.022*10^23= 401.07x 10^23moles

But each h20 moles has 10 electrons so it will be 4.01*10^26electrons

Then finally total charge will be

4.01*10^26electrons x 1.6*10^-19

= 6.416*10^ 8C

The magnitude of total charge will be "6.416×10⁸ C".

According to the question,

Density, d = 1.2 L

Volume, V = 1000

The mass will be:

→ Mass = Density × Volume

By substituting the values,

            = [tex]1.2\times 1000[/tex]

            = [tex]1200[/tex] g

Now,

The number of moles will be:

→ N = [tex]\frac{Mass}{Molar \ mass}[/tex]

      = [tex]\frac{1200}{18.02}[/tex]

      = [tex]66.6[/tex] mol

The total no. of water molecules be:

= [tex]66.6\times 6.022\times 10^{23}[/tex]

= [tex]401.07\times 10^{23}[/tex] moles

hence,

The total charge be:

= [tex]4.01\times 10^{26}\times 1.6\times 10^{-19}[/tex]

= [tex]6.416\times 10^8[/tex] C

Thus the above response is correct.

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Answer:

i. Geodynamo

ii. Gravitational energy conversion

Explanation:

The outer core of the Earth is believed to be in molten form, consisting of mainly iron and nickel. The reaction (mixture) between these components or elements generates conventional currents which is maintained by the gravitational energy produced in the process. Thus, magnetic fields are generated continuously due to the continuous flow of electric current during the processes.

Answer:

Final velocity = 30 m/s

Explanation:

We are given;

Initial velocity; u = 0 m/s

Acceleration; a = 3 m/s²

Time; t = 10 seconds

From Newton's first law of motion, the final velocity is given by the formula;

v = u + at

Plugging in the relevant values gives;

v = 0 + (3 × 10)

v = 30 m/s

Answer:

57.42 N

Explanation:

We first find the acceleration knowing that it goes from rest to 8.3 m/s in 0.13 seconds,

Therefore, the acceleration is:

[tex]a=\frac{v_f-v_i}{time} =\frac{8.3-0}{0.13 } =63.8\,\,m/s^2[/tex]

Now we use this to calculate the average net force by multiplying mass times acceleration:

F = m * a = 0.9 (63.8) = 57.42 N