A pilot flies her route in two straight-line segments. The displacement vector A for the first segment has a magnitude of 243 km and a direction 30.0o north of east. The displacement vector for the second segment has a magnitude of 178 km and a direction due west. The resultant displacement vector is R = A + B and makes an angle ? with the direction due east. Using the component method, find (a) the magnitude of R and (b) the directional angle ?.
(a) R = km
(b) ? = degrees

Complete question:

A transverse wave on a rope is given by [tex]y \ (x, \ t) = (0.75 \ cm) \ cos \ \pi[(0.400 \ cm^{-1}) x + (250 \ s^{-1})t][/tex]. The mass per unit length of the rope is 0.0500 kg/m. Find the tension. Express your answer in newtons.

Answer:

The tension on the rope is 1.95 N

Explanation:

The general equation of a progressive wave is given as;

[tex]y \ (x,t) = A \ cos(kx \ + \omega t)[/tex]

Compare the given equation with the general equation of wave, the following parameters will be deduced.

A = 0.75 cm

k = 0.400π cm⁻¹

ω = 250π s⁻¹

The frequency of the wave is calculated as;

ω = 2πf

2πf = 250π

2f = 250

f = 250/2

f = 125 Hz

The wavelength of the wave is calculated as;

[tex]\lambda = \frac{2\pi}{k} \\\\\lambda = \frac{2\pi }{0.4 \pi} = 5 \ cm = 0.05 \ m[/tex]

The velocity of the wave is calculated as;

v = fλ

v = 125 x 0.05

v = 6.25 m/s

The tension on the rope is calculated as;

[tex]v = \sqrt{\frac{T}{\mu}} \\\\where;\\\\T \ is \ the \ tension \ of \ the \ rope\\\\\mu \ is \ the \ mass \ per \ unit \ length = 0.05 \ kg/m\\\\v^2 = \frac{T}{\mu} \\\\T = v^2 \mu\\\\T = (6.25)^2\times (0.05)\\\\T = 1.95 \ N[/tex]

Therefore, the tension on the rope is 1.95 N

Answer:

Let's define t = 0s (the initial time) as the moment when Car A starts moving.

Let's find the movement equations of each car.

A:

We know that Car A accelerations with a constant acceleration of 5m/s^2

Then the acceleration equation is:

[tex]A_a(t) = 5m/s^2[/tex]

To get the velocity, we integrate over time:

[tex]V_a(t) = (5m/s^2)*t + V_0[/tex]

Where V₀ is the initial velocity of Car A, we know that it starts at rest, so V₀ = 0m/s, the velocity equation is then:

[tex]V_a(t) = (5m/s^2)*t[/tex]

To get the position equation we integrate again over time:

[tex]P_a(t) = 0.5*(5m/s^2)*t^2 + P_0[/tex]

Where P₀ is the initial position of the Car A, we can define P₀ = 0m, then the position equation is:

[tex]P_a(t) = 0.5*(5m/s^2)*t^2[/tex]

Now let's find the equations for car B.

We know that Car B does not accelerate, then it has a constant velocity given by:

[tex]V_b(t) =20m/s[/tex]

To get the position equation, we can integrate:

[tex]P_b(t) = (20m/s)*t + P_0[/tex]

This time P₀ is the initial position of Car B, we know that it starts 100m ahead from car A, then P₀ = 100m, the position equation is:

[tex]P_b(t) = (20m/s)*t + 100m[/tex]

Now we can answer this:

1) The two cars will meet when their position equations are equal, so we must have:

[tex]P_a(t) = P_b(t)[/tex]

We can solve this for t.

[tex]0.5*(5m/s^2)*t^2 = (20m/s)*t + 100m\\(2.5 m/s^2)*t^2 - (20m/s)*t - 100m = 0[/tex]

This is a quadratic equation, the solutions are given by the Bhaskara's formula:

[tex]t = \frac{-(-20m/s) \pm \sqrt{(-20m/s)^2 - 4*(2.5m/s^2)*(-100m)} }{2*2.5m/s^2} = \frac{20m/s \pm 37.42 m/s}{5m/s^2}[/tex]

We only care for the positive solution, which is:

[tex]t = \frac{20m/s + 37.42 m/s}{5m/s^2} = 11.48 s[/tex]

Car A reaches Car B after 11.48 seconds.

2) How far does car A travel before the two cars meet?

Here we only need to evaluate the position equation for Car A in t = 11.48s:

[tex]P_a(11.48s) = 0.5*(5m/s^2)*(11.48s)^2 = 329.48 m[/tex]

3) What is the velocity of car B when the two cars meet?

Car B is not accelerating, so its velocity does not change, then the velocity of Car B when the two cars meet is 20m/s

4)  What is the velocity of car A when the two cars meet?

Here we need to evaluate the velocity equation for Car A at t = 11.48s

[tex]V_a(t) = (5m/s^2)*11.48s = 57.4 m/s[/tex]

Answer:

Well a meter stick has increments of a centimeter, and since 1 cm=0.01m he should record it as 4.02m(b)

Explanation:

Answer:

a n c

Explanation:

Answer:

C. When an object floats, it does not displace its entire volume.

Explanation:

Buoyancy can be defined as an upward force which is created by the water displaced by an object.

According to Archimede's principle, it is directly proportional to the amount (weight) of water that is being displaced by an object.

Basically, the greater the amount of water an object displaces; the greater is the force of buoyancy pushing the object up. The buoyancy of an object is given by the formula;

[tex] Fb = pgV [/tex]

[tex] But, \; V = Ah [/tex]

[tex] Hence, \; Fb = pgAh [/tex]

Where;

Fb = buoyant force of a liquid acting on an object.

g = acceleration due to gravity.

p = density of the liquid.

v = volume of the liquid displaced.

h = height of liquid (water) displaced by an object.

A = surface area of the floating object.

The unit of measurement for buoyancy is Newton (N).

Additionally, the density of a fluid is directly proportional to the buoyant force acting on it i.e as the density of a liquid decreases, buoyancy decreases and vice-versa.

Furthermore, an object such as a boat, ship, ferry, canoe, etc, are able to float because the volume of water they displace weigh more than their own weight. Thus, if a boat or any physical object weighs more than the volume of water it displaces, it would sink; otherwise, it floats.

In conclusion, the true statement is that when an object floats, it does not displace its entire volume.

efficiency=work output/work input×100

since it exhausts(use up)3000j of heat that's the work input and the 1500j is the work input

efficiency=1500/3000×100

=50%

Answer:

24 cm/s

Explanation:

Applying

Pythagoras theorem,

a² = b²+c²............. Equation 1

Where a = resultant, b = vertical component, c = horizontal component

From the question,

Given: a = 26 cm/s, c = 10 cm/s

Substitute these values into equation 1

26² = b²+10²

676 = b²+100

b² = 676-100

b² = 576

b = √576

b = 24 cm/s

Answer:

Smaller and upside down

Explanation:

To answer the question, we must recognise that the characteristics of the image formed by a convex lens depends on the position of the object from the lens.

From the diagram given in the question above, the following data were obtained:

1. The image is smaller than the object.

2. The image is inverted i.e upside down.

3. The image is closer to the lens

4. The image between 2f and f

Now, considering the options given in question above, the correct answer to the question is:

The image is smaller and upside down.

Answer:

temperature

Explanation:

temperature change forms different elements and different element sustain different colour

Answer:

a)   a = 91.4 m / s²,  b)    t = 0.175 s, c)  

Explanation:

a) This is a kinematics exercise

           v² = vox ² + 2a (x-xo)

           a = v² - 0/2 (x-0)

let's calculate

          a = 16² / 2 1.4

          a = 91.4 m / s²

b) the shooting time

          v = vox + a t

          t = v-vox / a

          t = 16 / 91.4

          t = 0.175 s

c) let's use Newton's second law

          F = ma

          F = 7.9 91.4

          F = 733 N

Answer:

False

Explanation:

You have a circle so think back to circular motion. Theres 2 directions, centripetal and tangential. The problem tells you there's a constant tangential speed so tangential acceleration is 0. However there is a centripetal acceleration acting on the ball that holds it in its circular motion (i.e. tension, or gravity). Since centripetal is perpendicular to the tangential direction, acceleration and velocity are in different directions.

Answer:

Tempered glass

Explanation:

When warmed, an amorphous substance has a non-crystalline architecture that differentiates from its isochemical liquid, but this does not go through structural breakdown or the glass transition.

Answer:The SI system is based on the number 10 as well as multiples and products of 10. This makes it much easier to use, and so it has been the accepted system in scientific and technical applications. The English system is more complicated as relationships between units of the same quantity aren't uniform.

Explanation:

Answer:

The metric system is an internationally agreed decimal system of measurement while The International System of Units (SI) is the official system of measurement in almost every country in the world

Answer:

Explanation:

Intensity of sound = sound energy emitted by source / 4 π d² , where d is distance of the source .

A )

Intensity of sound at 1 m distance = 60 /4 π d²

d = 1 m

Intensity of sound at 1 m distance = 60 /(4 π 1²)

= 4.78 W m⁻² s⁻¹

B )

Intensity of sound at 1.5 m distance = 60 /4 π d²

d = 1.5  m

Intensity of sound at 1 m distance = 60 /(4 π 1.5²)

= 2.12 W m⁻² s⁻¹

C )

Intensity of sound due to 4 speakers at 1.5 m distance = 4 x 60 /4 π d²

d = 1.5  m

= 4 x 60 /(4 π 1.5²)

= 8.48 W m⁻² s⁻¹

D )

Intensity of sound due to .06 W speaker must be 10⁻¹² W s ⁻² . Let the distance be d .

.06 /4 π d² = 10⁻¹²

d² = .06 /4 π 10⁻¹²

d = 6.9 x 10⁴ m .

Answer:

The maximum height is 0.33 m.

Explanation:

initial velocity, u = 8 m/s

final velocity, v = 0 m/s

10% of  kinetic energy is lost in friction.

The kinetic energy used to move up the top,

KE = 10 % of 0.5 mv^2

KE = 0.1 x 0.5 x m x 8 x 8 = 3.2 m

Let the maximum height is h.

Use conservation of energy

KE at the bottom = PE at the top

3.2 m = m x 9.8 x h

h = 0.33 m  

The height traveled vertically up the hill by the ball when it stops is 0.327 meter.

Given the following data:

Scientific data:

To determine how far (height) vertically up the hill the ball reaches when it stops:

By applying the law of conservation of energy, we have:

Kinetic energy lost at the bottom = Potential energy gained at the top.

Mathematically, the above expression is given by the formula:

[tex]0.1 \times \frac{1}{2} mv^2 = mgh\\\\0.1 \times \frac{1}{2} v^2 = gh\\\\h=\frac{0.1v^2}{2g}[/tex]

Substituting the given parameters into the formula, we have;

[tex]h=\frac{0.1 \times 8^2}{2\times 9.8} \\\\h=\frac{0.1 \times 64}{19.6} \\\\h=\frac{6.4}{19.6}[/tex]

Height, h = 0.327 meter.

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Answer: The focal length of the lens is 2.60 cm

Explanation:

The equation for lens formula follows:

[tex]\frac{1}{f}=\frac{1}{v}-\frac{1}{u}[/tex]

where,

f = focal length = ? cm

v = image distance = 2.9 cm

u = Object distance = -25 cm

Putting values in above equation, we get:

[tex]\frac{1}{f}=\frac{1}{2.9}-\frac{1}{(-25)}\\\\\frac{1}{f}=\frac{1}{2.9}+\frac{1}{(25)}\\\\\frac{1}{f}=\frac{25+2.9}{2.9\times 25}\\\\f=\frac{72.5}{27.9}=2.60cm[/tex]

Hence, the focal length of the lens is 2.60 cm

Answer:The answer is C

Explanation:

Answer:

I = 0.25 A

Explanation:

Given that,

Three 15 ohms and two 25 ohms light bulbs and a 24 V battery are connected in a series circuit.

In series combination, the equivalent resistance is given by :

[tex]R=R_1+R_2+R_3+....[/tex]

So,

[tex]R=15+15+15+25+25\\\\=95\ \Omega[/tex]

The current each resistor remains the same in series combination. It can be calculated using Ohm's law i.e.

V = IR

[tex]I=\dfrac{V}{R}\\\\I=\dfrac{24}{95}\\\\I=0.25\ A[/tex]

So, the current of 0.25 A passes through each bulb.

Answer:

Option (a), (d) are correct.

Explanation:

Frequency, f = 220 Hz

Resonant frequency = 660 Hz

The next frequency of stopped organ pipe is

2f, 3 f, 4 f ....

= 2 x 220 , 3 x 220 , 4 x 220 ....

= 440 Hz, 660 Hz, 880 Hz

So, the option (a) is correct.

The next resonant frequency of open organ pipe is

3 f, 5 f,...

= 3 x 220, 5 x 220 , ..

= 660 Hz, 1100 Hz,...

So, option (d) is correct.

The desk is in equilbrium, so Newton's second law gives

∑ F (horizontal) = p - f = 0

∑ F (vertical) = n - mg = 0

==>   n = mg

==>   p = f = µn = µmg = 0.400 (80.0 kg) g = 313.6 N

The student pushes the desk 3.00 m, so she performs

W = (313.6 N) (3.00 m) = 940.8 Nm ≈ 941 J

of work.

Answer:

   P = 10135.6 Pa

Explanation:

For this exercise we use that the pressure varies with the height

           P = P₀ + ρ g h

where h is the height from the head to the heart, which is approximately

h = 40 cm = 0.40m  and P₀ is the head pressure P₀ = 6000 Pa

          P = 6000 + 1055 9.8 0.40

          P = 6000 + 4135.6

          P = 10135.6 Pa

Answer:

The magnitude of the electric field is same while the direction at the left and at the right is opposite to each other.

Explanation:

The direction of the electric field due to the dipole on the axial line is same as  the direction of dipole moment.

The magnitude of the electric field due to an electric dipole on its axial line is

[tex]E=\frac{2kp}{r^3}[/tex]

where, k is the constant, p is the electric dipole moment and r is the distance from the center of dipole.

The magnitude of the electric field is same while the direction at the left and at the right is opposite to each other.  

Answer:

Hydroelectricity

Explanation:

Because of flooding of water, we can assume that the electricity was generated by Water which is known as Hydroelectricity.

We can presume that the energy was produced by water because of the flooding of the water, which is a process known as hydroelectricity.

Hydroelectric power, often known as hydropower, is the name given to electricity generated by turbines that turn the potential energy of falling or swiftly running water into mechanical energy. As of 2019, hydropower accounted for more than 18% of the world's total power generation capacity, giving it the most frequently used renewable power source in the early 21st century.

When water is used to produce energy, it is first gathered or stored at a higher altitude and then transported through extensive pipelines or tunnels (called pen stocks) to a lower level; the difference between these two altitudes is referred to as the head. The falling water triggers the rotation of turbines at the bottom of its descent through the pipes.

To know more about Hydroelectricity:

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30.1 N

Explanation:

Given:

[tex]W_1 = 16\:\text{N}[/tex]

[tex]W_2 = 8\:\text{N}[/tex]

Let's write the components of the net forces at the intersections. Note that the system is equilibrium so all the net forces are zero.

Forces involving W1:

[tex]x:\:\:\:-T_1 + T_3\cos \alpha = 0\:\: \\ \text{or}\:\:T_2 = T_3\cos \alpha\:\:\:\:\:(1)[/tex]

[tex]y:\:\:\:T_3\sin \alpha - W_1 = 0\:\:\: \\ \text{or}\:\:\:T_3\sin \alpha = W_1\:\:\:\:\:\:(2)[/tex]

Forces involving W2:

[tex]x:\:\:\:T_1\sin 53 - T_3\sin \alpha = W_2\:\:\:\:\:\:\:(3)[/tex]

[tex]y:\:\:\:T_4 - T_1\cos 53 - T_3\cos \alpha = 0\:\:\:\;(4)[/tex]

Substitute (2) into (3) and we get

[tex]T_1\sin 53 - W_1 = W_2[/tex]

Solving for [tex]T_1[/tex],

[tex]T_1 = \dfrac{W_1 + W_2}{\sin 53} = 30.1\:\text{N}[/tex]

Answer:

  v = 2.75 10⁴ m / s

Explanation:

For this exercise we must use Kepler's third law which is an application of Newton's second law to the solar system

            F = ma

where force is the force of gravity

            F = [tex]G \frac{m M}{r^2}[/tex]

acceleration is centripetal

             a = [tex]\frac{v^2}{r}[/tex]

we substitute

           G m M / r² = m v² / r

           [tex]\frac{GM}{r}[/tex] = v²

           v = [tex]\sqrt{GM/r}[/tex]

indicate that the radius of the orbit is r = 1.17 AU, let's reduce to the SI system

            r = 1.17 AU (1.496 10¹¹ m / 1 AI) = 1.76 10¹¹ m

let's calculate

         v = [tex]\sqrt{\frac{6.67 \ 10^{-11} 1.991 \ 10^{30} }{ 1.76 \ 10^{11}} }[/tex]Ra (6.67 10-11 1.991 10 30 / 1.76 10 11

         v = [tex]\sqrt{7.5454 \ 10^8 }[/tex]ra 7.5454 10 8

         v = 2.75 10⁴ m / s

Distance travelled by a body in unit time is called speed. it is a scalar quantity because it can be specified only by magnitude.