A rocket train car that is 30 m long is traveling from Los Angeles to New York at v=0.5c when a light at the center of the car flashes. When the light reaches the front of the car, it immediately rings a bell. Light reaching the back of the car immediately sounds a siren. A bicyclist waiting to cross the tracks sees the light in front of her at the instant when it flashes. Choose frame S' so that its origin is located at the center of the train. Take the direction of motion of the train (eastward) to be the positive direction of x'. Let the instant when the light flashes be t′=0s.

Required:
What are (x′A,t′A) and (x′B,t′B), the spacetime coordinates of event A and B in S'?

Explanation:

T = 2π√(m/k)

T = 2π√(16 kg / 4 N/m)

T = 4π s

T ≈ 12.6 s

Answer:

20 m/s.

Explanation:

Data obtained from the question include the following:

Initial position (d1) = 20 m

Final position (d2) = 60 m

Initial time (t1) = 1 sec

Final time (t2) = 3 secs

Velocity (v) =?

Next, we shall determine the change in position (Δd). This can be obtained as follow:

Initial position (d1) = 20 m

Final position (d2) = 60 m

Change in position (Δd) =?

Change in position (Δd) = d2 – d1

Change in position (Δd) = 60 – 20

Change in position (Δd) = 40 m

Next, we shall determine the change in time (Δt). This can be obtained as follow:

Initial time (t1) = 1 sec

Final time (t2) = 3 secs

Change in time (Δt) =?

Change in time (Δt) = t2 – t1

Change in time (Δt) = 3 – 1

Change in time (Δt) = 2 secs.

Finally, we shall determine the velocity of the object as follow:

Change in position (Δd) = 40 m

Change in time (Δt) = 2 secs.

Velocity (v) =?

Velocity (v) = Change in position (Δd) /Change in time (Δt)

v = Δd/Δt

v = 40/2

v = 20 m/s

Therefore, the velocity of the object between 1 and 3 secs is 20 m/s

Answer:

0.784 A

Explanation:

From the question,

Note that the current in the circuit is the same as the current flowing through the inductor since they are both connected in series.

I = VL/XL....................... Equation 1

Where I = current flowing through the circuit, VL = Voltage drop across the inductor,  XL = reactance of the inductor.

XL = 2πfL................. Equation 2

Given: f = 28.9 Hz, L = 1.07 H, π = 3.143

XL = 2(3.143)(28.9)(1.07)

XL = 194.38 Ω.

VL = V-Vf

VL = 170-17.6

VL = 152.4 V

Substitute these values into equation 1

I = 152.4/194.38

I = 0.784 A

The current in the circuit when combination is connected  should be 0.784 A.

SInce

we know that

I = VL/XL....................... Equation 1

Here,

I = current flowing through the circuit,

VL = Voltage drop across the inductor,  

XL = reactance of the inductor.

And,

XL = 2πfL................. Equation 2

Here

f = 28.9 Hz, L = 1.07 H, π = 3.143

So,

XL = 2(3.143)(28.9)(1.07)

XL = 194.38 Ω.

Now

VL = V-Vf

VL = 170-17.6

VL = 152.4 V

Now

I = 152.4/194.38

I = 0.784 A

hence, The current in the circuit when combination is connected  should be 0.784 A.

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Answer:

32.1

Explanation:

NOTE: You did not state the angle of incidence, and thus, I will be using 45° as my angle of incidence, all you need to do is replace it with your own value if it's different.

To solve this question, we are going to be using Snell's Law.

Snell's law describes the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.

Snell's law is mathematically given as

sin(A1)/sin(A2) = n2/n1, where

n1 = incidence index

n2 = refracted index

A1 = incidence angle

A2 = refracted angle

The refraction index of oil is 1.15, and that of water is 1.33, so

if we take oil first,

sin A2 = (n1.sinA1)/n2

sin A2 = (1 * sin 45)/1.15

sin A2 = 0.7071/1.15

sin A2 = 0.6149

A2 = sin^-1 0.6149

A2 = 37.9°

Then

sin A3 = (1.15 * sin 37.9) / 1.33

sin A3 = (0.6149 * 1.15) / 1.33

sin A3 = 0.7071 / 1.33

sin A3 = 0.5317

A3 = sin^-1 0.5317

A3 = 32.1

Answer:

7.8x10-12N

Explanation:

We know that

Magnetic force = F = qVB

And

Also Kinetic energy K.E is

E = (1/2)mV²

So making v subject

V = √(2E / m)

And

E = KE = 2MeV

= 2 × 106 eV

= 2 × 106 × 1.6 × 10–19 J

= 3.2 × 10–13 J

And then

V= √2x3.2E-13/1.6E-27

1.9E7m/s

Given that

mass of proton = 1.6 × 10–27 kg,

Magnetic field strength B = 2.5 T.

So F= qBv sinစ

=

So F = 1.6 × 10–19 × 2.5 × 1.9 x10^7 x sin 90°

= 7.8 x 10^-12N

Answer:

8*10^-12

Explanation:

Given that

Energy of proton, K = 2 MeV = 2 * 1.6*10^-19 *10^6 = 3.2*10^-13

magnetic field strength, B = 2.5 T

mass of proton, m = 1.67*10^-27 kg

K = ½mv², making v² the subject of formula by rearranging, we have

v² = 2k/m

v² = (2 * 3.2*10^-13) / 1.67*10^-27

v² = 6.4*10^-13 / 1.6*10^-27

v² = 4*10^14

v = √4*10^14

v = 2*10^7 m/s

f = qvbsinθ, where

θ = 90

v = 2*10^7 m/s

b = 2.5 T

q = 1.6*10^-19

f = 1.6*10^-19 * 2*10^7 * 2.5 sin 90

f = 8*10^-12 N

thus, the force on the proton is 8*10^-12

Answer:

eating instrument must be: HARDNESS,  INERT, NOT TOXIC

eating tools: digested by the body

Explanation:

An eating instrument must be able to contain food, so it must have a good HARDNESS, besides it must be poorly absorbent of heat and the most important must be INERT, not react with food or be NOT TOXIC to humans.

Additionally, for a spoon to be edible, it must be able to be digested by the body, in general they are made with a starch base, so that the non-digestible parts of it have not been toxic to the body and can be eliminated from it.

There are numerous features of a spoon but these properties must an edible spoon

have

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Answer:

use the distance formula d=v*t

d= distance

v = velocity

t = time = t1 + t2 = 2h +3h = 5 hours (total time given)

At 65 km/h distance (d1) answer:

d1 = (65 km/h)*( 2h) = 130 km

Total Distance:

so d1 + d2 = Dtotal

Dtotal = 130 km + (78 km/h)*3 = 130 km + 234 km = 364 km

Answer:

The  value is  [tex]d = 0.000293 \ m[/tex]

Explanation:

From the question we are told that

   The wavelength is  [tex]\lambda = 633 \ nm = 633 *10^{-9} \ m[/tex]

    The  distance of the screen is  [tex]D = 2.5 \ m[/tex]

    The  order of the bright fringes is  [tex]n = 10[/tex] (10  fringe + central maximum = eleven bright fringes )

      The distance between the fringe is  [tex]y = 54 \ mm = 0.054 \ m[/tex]

Generally the condition for constructive interference is  

        [tex]d sin \theta = n * \lambda[/tex]

=>     [tex]d = \frac{n * \lambda}{sin \theta}[/tex]

Now  from the SOHCAHTOA rule the angle  [tex]sin \theta[/tex] is mathematically represented as

      [tex]sin (\theta) = \frac{y}{D}[/tex]

So  

          [tex]d = \frac{n * \lambda}{\frac{y}{D} }[/tex]

=>       [tex]d = \frac{10 * 633 *10^{-9}}{\frac{0.054}{ 2.5} }[/tex]

=>      [tex]d = 0.000293 \ m[/tex]

Answer:

initial velocity (u) = 200m/s

final velocity (v) = 350 m/s

time (t) = 15s

acceleration (a) = ?

NOW,

a=v-u/t

a= 350-200/15

a= 50/15

a= 3.3333

Explanation:

it's too easy just u need to understand the question . and go according to it's content .

main thing to memorize is it's simple formula.

I HAVE SOLVE THIS QNA. IN VERY

SIMPLE AND UNDERSTANDABLE FORM.

I høpë u hađ uņdērstøöď ťhìs şølutîóñ

:verý ×wəłł.

Answer:

The velocity of the particle will be downward.

Explanation:

Given that,

The velocity of a particle is v₁. It is accelerated from 1 to 2.

If it moves away from point 2 on its way then

We need to find the velocity of particle

According to figure,

A particle moves downward from 1 to 2 with the velocity v₁ and after that the particle moves downward from 2 to 3 with the velocity v₂.

Hence, The velocity of the particle will be downward.

Explanation:

Density = mass / volume

ρ = 11.1 g / 44.5 mL

ρ = 0.249 g/mL

Answer:

a) wavelength = 656.3 nm

b)  the value of Rydberg's constant for this measurement is 1.097 × 10⁷ m⁻¹

Explanation:

Given that;

angle of diffraction Θₓ = 22.78°

incident angle Θ₁ = 0

slit separation d  = 5900 lines per cm = 1/5900 cm = 10⁻²/5900 m = 0.01/5900 m

order of diffraction n = 1

wavelength λ = ?

to find the wavelength, we use the expression

λ = d (sinΘ₁ + sinΘₓ) / n

To find the wavelength λ;

λ = 0.01/5900 × (sin0 + sin22.78° )

λ = 6.5626 × 10⁻⁷ m

λ = 656.3 x 10⁻⁹ m

∴ λ = 656.3 nm

b)

According Balnur's  series spectral lines; n₁ = 3, n₂ = 2 and

λ = R [ 1/n₂² - 1/n₁²]

where  R is Rydberg's constant

from λ = R [ 1/n₂² - 1/n₁²]

R = 1/λ [n₂²n₁² / n₁² - n₂²]

R = 10⁹/ 656.3 [ 9 × 4 / 9 - 4 ]

R = 1.097 × 10⁷ m⁻¹

Therefore the value of Rydberg's constant for this measurement is 1.097 × 10⁷ m⁻¹

Explanation:

Momentum is conserved.

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Initially, both the astronaut and the tool are at rest, so u₁ = u₂ = 0 m/s.

After throwing the tool, the tool has a velocity of v₂ = 3.20 m/s.

(68.5 kg) (0 m/s) + (2.25 kg) (0 m/s) = (68.5 kg) v + (2.25 kg) (3.20 m/s)

0 = (68.5 kg) v + 7.2 kg m/s

v = -0.105 m/s

The astronaut moves at a speed of 0.105 m/s in the opposite direction.

The speed and the direction of the astronaut is 0.105 m/s in opposite direction to the motion of the tool.

Note: The momentum of the astronaut is equal and opposite to the momentum of the tool

To calculate the speed and the direction of the astronaut, we use the formula below.

Formula:

Where:

make V the subject of the equation

From the question,

Given:

Substitute these values into equation 2

Hence, The speed and the direction of the astronaut is 0.105 m/s in opposite direction to the motion of the tool.

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Answer:

6 and 14 respectively

Explanation:

proton number = atomic number

mass number = proton number + neutron number

since

Explanation:

The de broglie wavelength is given by :

[tex]\lambda=\dfrac{h}{p}[/tex]

Here,

h is Planck's constant

p is momentum

Momentum and De-Broglie wavelength has inverse relationship. If momentum of an electron double, its wavelength gets half.

Answer:

160 Hz

Explanation:

Fundamental frequency, [tex]f_{0}[/tex], is the lowest frequency that can be obtained from the stretched string. While higher frequencies are termed harmonics or overtones.

Since the string has three equal segments, the frequency generated, [tex]f_{2}[/tex], is the second harmonic but third overtone.

From the relationship between [tex]f_{0}[/tex] and [tex]f_{2}[/tex], we have;

                          [tex]f_{2}[/tex] = 3[tex]f_{0}[/tex]

⇒                     480 = 3[tex]f_{0}[/tex]

                           [tex]f_{0}[/tex]  = 160

The fundamental frequency of vibration for the string is 160 Hz.

Answer:

Star characteristics consider physical characteristics such as stellar mass, size, surface temperature, and luminosity .

Answer:

They are made of gases.

Explanation:

Edg 2020

Answer:

Power, P = 307.31 W

Explanation:

It is given that,

Kasek climb at an angle of 6° with the horizontal at a steady speed of 4.0 m/s.

The total mass of bicycle and Kasek is 75 kg

We need to find the Kasek's power output to climb the same hill at the same speed. The angle is made with the horizontal. It means that,

F = F sinθ

So,

Power output is given by :

[tex]P=mg\sin\theta\times v\\\\P=75\times 9.8\times \sin(6)\times 4\\\\P=307.31\ W[/tex]

So, Kasek's power output to climb the same hill is 307.31 W.

Answer:

0.228 nm

Explanation:

Atomic mass number of copper = 64

but an atomic mass unit = 1.66 x 10^-27 kg

therefore, the mass of the copper atom m = 64 x 1.66 x 10^-27 kg = 1.06 x 10^-25 kg

The number of atoms in this mass n = ρ/m

where ρ is the density of copper = 8.96 x 10^3 kg/m^3

==> n = (8.96 x 10^3)/(1.06 x 10^-25) = 8.45 x 10^28 atoms/m^3

We know that the volume occupied by this amount of atoms n = [tex]a^{3}[/tex]

where a is the lattice constant

equating, we have

8.45 x 10^28 = [tex]a^{3}[/tex]

a = 4.389 x 10^9

we also know that

d =  1/a

where d is the smallest distance between the two copper atom.

d = 1/(4.389 x 10^9) = 2.28 x 10^-10 m

==> 0.228 nm

Answer:

kinetic energy = 0.1168 J

Explanation:

From Hooke's law, we know that ;

F = kx

k = F/x

We are given ;

Mass; m = 1.95 kg

Spring stretch; d = x = 0.0865

So, Force = mg = 1.95 × 9.81

k = 1.95 × 9.81/0.0865 = 221.15 N/m

Now, initial energy is;

E1 = mgL + ½k(x - L)²

Also, final energy; E2 = ½kx² + ½mv²

From conservation of energy, E1 = E2

Thus;

mgL + ½k(x - L)² = ½kx² + ½mv²

Making the kinetic energy ½mv² the subject, we have;

½mv² = mgL + ½k(x - L)² - ½kx²

We are given L=0.0325 m

Plugging other relevant values, we have ;

½mv² = (1.95 × 9.81 × 0.0325) + (½ × 221.15(0.0865 - 0.0325)² - ½(221.15 × 0.0865²)

½mv² = 0.62170875 + 0.3224367 - 0.82734979375

½mv² = 0.1168 J

Answer:

see from this analysis, the apparent weight of the body is lower due to the push created by the air brujuleas

Explanation:

We will propose this exercise using Archimedes' principle, which establishes that the thrust on a body is equal to the volume of the desalted liquid.

          B = ρ g V

The weight of a submerged body is the net force between the weight and the thrust

          F_net = W - B

we can write the weight as a function of the density

          ρ_body = m / V

         m =  ρ_body V

         W = mg

         W =  ρ _body g V

we substitute

         F_net= ( ρ_body -  ρ _fluid) g V

In general this force is directed downwards, we can call this value the apparent weight of the body. This is the weight of the submerged body.

          W_aparente = ( ρ_body -  ρ _fluid) g V

If some air bubbles formed in this body, the net force of these bubbles is

         F_net ’= #_bubbles ( ρ_fluido -  ρ_air) g V’

this force is directed upwards

whereby the measured force is

         F = W_aparente - F_air  

As we can see from this analysis, the apparent weight of the body is lower due to the push created by the air brujuleas

Answer:

1840:1

Explanation:

If m is the mass of the electron, and 1840m is the mass of the proton, then:

p₁ = p₂

m₁v₁ = m₂v₂

m v₁ = 1840m v₂

v₁ = 1840 v₂

The kinetic energy of the electron is:

KE₁ = ½ m₁ v₁²

KE₁ = ½ m (1840 v)²

KE₁ = 1692800 mv²

The kinetic energy of the proton is:

KE₂ = ½ m₂ v₂²

KE₂ = ½ (1840m) v₂²

KE₂ = 920 mv²

The ratio of the kinetic energies is:

KE₁ / KE₂

(1692800 mv²) / (920 mv²)

1840:1

Answer:

1.170*10^-3 m

3.23*10^-32 m

Explanation:

To solve this, we apply Heisenberg's uncertainty principle.

the principle states that, "if we know everything about where a particle is located, then we know nothing about its momentum, and vice versa." it also can be interpreted as "if the uncertainty of the position is small, then the uncertainty of the momentum is large, and vice versa"

Δp * Δx = h/4π

m(e).Δv * Δx = h/4π

If we make Δx the subject of formula, by rearranging, we have

Δx = h / 4π * m(e).Δv

on substituting the values, we have

for the electron

Δx = (6.63*10^-34) / 4 * 3.142 * 9.11*10^-31 * 4.95*10^-2

Δx = 6.63*10^-34 / 5.67*10^-31

Δx = 1.170*10^-3 m

for the bullet

Δx = (6.63*10^-34) / 4 * 3.142 * 0.033*10^-31 * 4.95*10^-2

Δx = 6.63*10^-34 / 0.021

Δx = 3.23*10^-32 m

therefore, we can say that the lower limits are 1.170*10^-3 m for the electron and 3.23*10^-32 for the bullet

Answer:

Explanation:

Magnitude of force per unit length of wire on each of wires

= μ₀ x 2 i₁ x i₂ / 4π r    where i₁ and i₂ are current in the two wires , r is distance between the two and  μ₀ is permeability .

Putting the values ,

force per unit length = 10⁻⁷ x 2 x i x 2i / ( 6 x 10⁻³ )

= .67 i² x 10⁻⁴

force on 3 m length

= 3 x .67 x 10⁻⁴ i²

Given ,

8 x 10⁻⁶ = 3 x .67 x 10⁻⁴ i²

i²  = 3.98 x 10⁻²

i = 1.995 x 10⁻¹

= .1995

=  0.2 A approx .

2 i = .4 A Ans .

The greater current is 0.4 A

Since the two long wires are parallel, the magnetic force, F on each wire is given by

F = μ₀I₁I₂L/2πd where μ₀ = permeability of free space = 4π × 10⁻⁷ H/m, I₁ = current in first wire, I₂ = current in second wire, L = length of section of wires = 3.0 m and d = separation distance of the wires = 6.0 mm = 6.0 × 10⁻³ m.

Given that F = 8.0 μN = 8.0 × 10⁻⁶ N and I₂ = 2I₁ (the current in one wire is twice the current in the other wire), we have

F = μ₀I₁I₂L/2πd

F = μ₀ 2I₁I₁L/2πd

F = μ₀I₁²L/πd

Since we require the current in the wire, we make I₁ subject of the formula.

So, I₁ = √(Fπd/μ₀L)

Substituting the values of the variables into the equation, we have

I₁ = √(Fπd/μ₀L)

I₁ = √[8.0 × 10⁻⁶ N × π × 6.0 × 10⁻³ m/(4π × 10⁻⁷ H/m × 3.0 m)]

I₁ = √[48.0π × 10⁻⁹ Nm/12π × 10⁻⁷ H]

I₁ = √[4 × 10⁻² Nm/H]

I₁ = 2 × 10⁻¹ A

I₁ = 0.2 A

Since I₂ is the greater current and I₂ = 2I₁,

I₂ = 2 × 0.2 A

I₂ = 0.4 A

So, the greater current is 0.4 A

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Answer:

Gravitational potential energy is converted into kinetic energy

Explanation:

During an avalanche, the  gravitational potential

energy of the snow on the mountain is converted into

kinetic energy as the snow cascades down.

The potential energy stored by the snow collected high in the mountain under the gravitational field created by our Earth, breaks loose and as it comes down acquiring velocity, it is converted into kinetic energy due to its accelerated motion

Answer:

2500 N

Explanation:

Draw a free body diagram of the bus.  There are three forces:

Weight force mg pulling down,

Normal force N pushing perpendicular to the ramp,

and friction force F pushing parallel to the ramp.

Sum of forces in the parallel direction:

∑F = ma

F − mg sin θ = 0

F = mg sin θ

F = (5000 N) (sin 30°)

F = 2500 N

Answer:

C

Explanation:

Rt= total resistance

we know that 1/Rt=1/R1+1/R2(from ohm's law)

Since, Rt=4 and R1=R2

we will get,

1/4=2/R2

R2=8

when in series Rt=R1+R2,

So, Rt=8+8=16 ohm's

If the two resistors are connected in series, then their equivalent resistance (in ohm) will be 16 ohms

The correct answer to the question is Option C. 16 ohms

Since the two resistors are identical, then

R₁ = R₂

•Equivalent resistance (Rₜ) = 4 Ohms

•Resistor 1 (R₁) = Resistor 2 (R₂) =?

In parallel connection,

Rₜ = (R₁ × R₂) / (R₁ + R₂)

4 = (R₁ × R₁) / (R₁ + R₁)

4 = R₁² / 2R₁

4 = R₁ / 2

Cross multiply

R₁ = 4 × 2

R₁ = 8 Ohms

Thus,

R₂ = R₁ = 8 Ohms

•Resistor 1 (R₁) = 8 Ohms

•Resistor 2 (R₂) = 8 Ohms

•Equivalent resistance (Rₜ) =?

In series connection,

Rₜ = R₁ + R₂

Rₜ = 8 + 8

Rₜ = 16 Ohms

Thus, the correct answer to the question is Option C. 16 ohms

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Explanation:

43 holits × (5 gorfs / 3 holits) × (2 queets / 7 gorfs) ≈ 20.5 queets

Answer:

A line with slope equal to the velocity.

Explanation:

If one is in the presence of constant velocity, that means that at the quotient between displacement and time elapsed is a constant value, therefore one can write the following equation:

[tex]\frac{displacement}{time} =constant[/tex]

therefore, solving for displacement we get:

[tex]displacement= constant \,*\, time[/tex]

which if plotted with displacement (D) on the vertical axis  and time (t) on the horizontal axis, renders a line with slope equal to the constant value of the velocity (v):

[tex]D=v\,*\,t[/tex]

Answer:

7.14 s

93.2 m/s, 24.9° below the horizontal

Explanation:

Given in the y direction:

Δy = -30 m

v₀ = 90 m/s sin 20° ≈ 30.8 m/s

a = -9.8 m/s²

Find: t

Δy = v₀ t + ½ at²

-30 m = (30.8 m/s) t + ½ (-9.8 m/s²) t²

4.9t² − 30.8t − 30 = 0

t = [ 30.8 ± √((-30.8)² − 4(4.9)(-30)) ] / 2(4.9)

t = 7.14 s

Find: vᵧ

v² = v₀² + 2aΔy

vᵧ² = (30.8 m/s)² + 2 (-9.8 m/s²) (-30 m)

vᵧ = -39.2 m/s

The magnitude of the velocity is:

v² = vₓ² + vᵧ²

v² = (90 m/s cos 20°)² + (-39.2 m/s)²

v = 93.2 m/s

The direction of the velocity is:

tan θ = vᵧ / vₓ

tan θ = (-39.2 m/s) / (90 m/s cos 20°)

θ = -24.9°