if A.B=A.C
does this imply that B must be equal to c ?
I need answer with example please ​

Answer:

[tex]K.E = (\frac{1}{2})Pv[/tex]

Explanation:

The momentum of a particle is defined as the product of its mass and velocity:

[tex]P = mv[/tex]   -------------------- equation (1)

where,

P = momentum of the particle

m = mass of the particle

v = velocity of the particle

The kinetic energy of the particle is given as follows:

[tex]K.E = (\frac{1}{2})mv^2\\\\K.E = (\frac{1}{2})v(mv)[/tex]

using equation (1), we get:

[tex]K.E = (\frac{1}{2})Pv[/tex]

Answer:

speed before landing = 3.9 m/s    (3 s.f.)

Explanation:

As rock is released from rest, u = 0 m/s     a = 1.62 m/s²     t = 2.4 s     v = ?

                      v = u + at

                      v = 0 + (1.62 x 2.4)

                      v = 3.888 = 3.9 s    (3 s.f.)

Hope this helps!

The speed of the rock before hitting the ground is 3.89 m/s

The given parameters;

acceleration due to gravity on moon, g = 1.62 m/s²

time taken for the object to fall, t = 2.4 s

To find:

The maximum height of fall of the rock is calculated as;

[tex]h = v_0t + \frac{1}{2} gt^2\\\\v_0 = 0\\\\h = \frac{1}{2} gt^2\\\\h = 0.5 \times 1.62 \times 2.4^2 \\\\h = 4.67 \ m[/tex]

The speed of the rock before hitting the ground is calculated as;

[tex]v_f^2 = v_0 ^2 + 2gh\\\\v_f^2 = 0 + 2\times 1.62 \times 4.67\\\\v_f^2 = 15.13\\\\v_f = \sqrt{15.13} \\\\v_f = 3.89 \ m/s[/tex]

Thus, the speed of the rock before hitting the ground is 3.89 m/s

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Answer:

12.5 Ns.

Explanation:

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

Force (F) = 250 N.

Time (t) = 0.05 s

Impulse =?

Impulse can be obtained by using the following formula:

Impulse = force × time

Impulse = 250 × 0.05

Impulse = 12.5 Ns

Thus, the Impulse applied to the ball is 12.5 Ns.

Answer:

E = 5.65 x 10¹⁰ N/C

Explanation:

First we need to find the total charge on the sphere. So, we use the following formula for that purpose:

[tex]q = \sigma V\\[/tex]

where,

q = total charge on sphere

V = Volume of Sphere = [tex]\frac{4}{3} \pi r^3 = \frac{4}{3} \pi (0.08\ m)^3 = 0.335\ m^3[/tex]

σ = volume charge density = 1.5 C/m³

Therefore,

[tex]q = (0.335\ m^3)(1.5\ C/m^3) \\q = 0.502 C[/tex]

Now, we use the following formula to find the electric field due to this charged sphere:

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

where.

E  = Electric Field Magnitude = ?

k = Coulomb's Constant = 9 x 10⁹ N.m²/C²

r = radius of sphere = 8 cm = 0.08 m

Therefore,

[tex]E = \frac{(9\ x\ 10^9\ Nm^2/C^2)(0.502 C)}{(0.08\ m)^2}\\\\[/tex]

E = 5.65 x 10¹⁰ N/C

Given that,

At 3.00 m from a source that is emitting sound uniformly in all directions, the sound level is 60.0 dB.

To find,

The distance from the source would the sound level be one-fourth the sound level at 3.00 m.

Solution,

The intensity from a source is inversely proportional to the distance.

Let I₁ = 60 dB, r₁ = 3 m, I₂ = 60/4 = 15 dB, r₂ =?

Using relation :

[tex]\dfrac{I_1}{I_2}=\dfrac{r_2^2}{r_1^2}\\\\r_2^2=\dfrac{I_1r_1^2}{I_2}\\\\r_2^2=\dfrac{60\times (3)^2}{15}\\\\r_2=6\ m[/tex]

So, at a distance of 6 m the sound level will be one fourth of the sound level at 3 m.

Answer:

[tex]v_{PB} = 130\ km/h[/tex]

Explanation:

Since, Alex is at rest. Therefore, the speed measured by him will be the absolute speed of car P. Therefore, taking easterly direction as positive:

[tex]Absolute\ Velocity\ of\ Car\ P = v_{P} = -78\ km/h[/tex]

And the absolute velocity of Barbara's Car is given as:[tex]Absolute\ Velocity\ of\ Barbara's\ Car = v_{B} = 52\ km/h[/tex]

Now, for the velocity of Car p with respect to the velocity of Barbara's Car can be given s follows:

[tex]Velocity\ of\ Car\ P\ measured\ by\ Barbara = v_{PB} = v_{B}-v_{P}\\\\v_{PB} = 52\ km/h-(-78\ km/h)[/tex]

[tex]v_{PB} = 130\ km/h[/tex]

Answer:

T large = 3T small

Explanation:

It's just 3 times larger

Answer: because of friction it will stop rolling completly

Explanation:

Explanation:

Single slit diffraction

Diffraction is the phenomenon of spreading out of waves as they pass through an aperture or around objects. Diffraction occurs when the size of the aperture or obstacle is of the same order of magnitude as the wavelength of the incident wave. For very small aperture sizes, the vast majority of the wave is blocked. in case of  large apertures the wave passes by or through the obstacle without any significant diffraction.

Answer:

17.71N/m

Explanation:

The period of the spring is expressed according to the expression;

[tex]T = 2 \pi \sqrt{\frac{m}{k} } \\[/tex]

m is the mass of the object

k is the force constant

Given

m = 5.50kg

T = 3.50s

Substitute into the formula;

[tex]T = 2 \pi \sqrt{\frac{m}{k} } \\3.5 = 2 (3.14) \sqrt{\frac{5.5}{k} } \\3.5 = 6.28 \sqrt{\frac{5.5}{k} } \\\frac{3.5}{6.28} = \sqrt{\frac{5.5}{k} } \\0.557 = \sqrt{\frac{5.5}{k} } \\square \ both \ sides\\0.557^2 = (\sqrt{\frac{5.5}{k} })^2 \\0.3106 = \frac{5,5}{k}\\k = \frac{5.5}{0.3106}\\k = 17.71N/m[/tex]

Hence the force constant of the spring is 17.71N/m

Answer:

Plane mirror

Explanation:

A virtual image is a copy of an object formed at the location from which the light rays appear to come.

Given that,

Mass of student 1, m₁ = 90 kg

Mass of student 2, m₂ = 60 kg

Speed of student 1, v₁ = 5 m/s

To find,

The velocity of the other student.

Solution,

Using the conservation of momentum to find the velocity of the other student. Let it is v₂.

[tex]m_1v_1=m_2v_2\\\\v_2=\dfrac{m_1v_1}{m_2}\\\\v_2=\dfrac{90\times 5}{60}\\\\=7.5\ m/s[/tex]

So, the velocity of the other student is 7.5 m/s.

Answer:

The skier will be moving at 13.31 m/s.

Explanation:

To calculate the velocity of the skier we need to find the acceleration, as follows:

[tex] \Sigma F = ma [/tex]

[tex] F_{r} - F_{f} = ma [/tex]

Where:

[tex] F_{r}[/tex]: is the force due to the rope = 365 N

[tex] F_{f}[/tex]: is the combined average frictional force = 190 N

m: is the mass = 75.0 kg

[tex] a = \frac{365 N - 190 N}{75.0 kg} = 2.33 m/s^{2} [/tex]

Now, we can calculate the velocity of the skier by using the following kinematic equation:

[tex] v_{f}^{2} = v_{0}^{2} + 2ad [/tex]

Where:

[tex] v_{f}[/tex]: is the final velocity =?

[tex] v_{0}[/tex]: is the initial velocity = 0 (the skier is initially at rest)

d: is the distance = 38.0 m

[tex] v_{f} = \sqrt{2*2.33 m/s^{2}*38.0 m} = 13.31 m/s [/tex]

Therefore, the skier will be moving at 13.31 m/s.

I hope it helps you!                                                                                  

Answer:

6

Explanation:

The magnetic field inside a solenoid is given by the following formula:

[tex]B = \mu_{0}nI[/tex]

where,

B = Magnetic Field Inside Solenoid

μ₀ = permittivity of free space

n = No. of turns per unit length

I = Current Passing through Solenoid

For Solenoid 1:

[tex]B_{1} = \mu_{0}n_{1}I ------------------- equation 1[/tex]

For Solenoid 2:

n₂ = 6n₁

Therefore,

[tex]B_{1} = \mu_{0}n_{2}I\\B_{1} = 6\mu_{0}n_{1}I ----------------- equation 2[/tex]

Diving equation 1 and equation 2:

[tex]\frac{B_{2}}{B_{1}} = \frac{6\mu_{0}nI}{\mu_{0}nI}\\\\\frac{B_{2}}{B_{1}} = 6[/tex]

Hence, the correct option is:

6

The ratio of the magnetic fields in interior 2 to interior 1 will be

[tex]\dfrac{B_2}{B_1} =\dfrac{6}{1}[/tex]

The formula for the magnetic fields inside the solenoid will be given:

[tex]B=\mu_onI[/tex]

here,

B = Magnetic Field Inside Solenoid

μ₀ = permittivity of free space

n = No. of turns per unit length

I = Current Passing through Solenoid

For the first Solenoid

[tex]B_1=\mu_on_1I[/tex]..................(1)

For the second solenoid

[tex]n_2=6n_1[/tex]

Now

[tex]B_2=\mu_on_2I[/tex]

[tex]B_2=\mu_o(6n_1)I[/tex]..................(2)

Diving equation 1 and equation 2:

[tex]\dfrac{B_2}{B_1} =\dfrac{\mu_o(6n_1)I}{\mu_on_2I}[/tex]

[tex]\dfrac{B_2}{B_1} =6[/tex]

Thus the ratio of the magnetic fields in interior 2 to interior 1 will be

[tex]\dfrac{B_2}{B_1} =\dfrac{6}{1}[/tex]

To know more about the Magnetic field of solenoids follow

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Answer:

W = - 118.24 J (negative sign shows that work is done on piston)

Explanation:

First, we find the change in internal energy of the diatomic gas by using the following formula:

[tex]\Delta\ U = nC_{v}\Delta\ T[/tex]

where,

ΔU = Change in internal energy of gas = ?

n = no. of moles of gas = 0.0884 mole

Cv = Molar Specific Heat at constant volume = 5R/2 (for diatomic gases)

Cv = 5(8.314 J/mol.K)/2 = 20.785 J/mol.K

ΔT = Rise in Temperature = 18.8 K

Therefore,

[tex]\Delta\ U = (0.0884\ moles)(20.785\ J/mol.K)(18.8\ K)\\\Delta\ U = 34.54\ J[/tex]

Now, we can apply First Law of Thermodynamics as follows:

[tex]\Delta\ Q = \Delta\ U + W[/tex]

where,

ΔQ = Heat flow = - 83.7 J (negative sign due to outflow)

W = Work done = ?

Therefore,

[tex]-83.7\ J = 34.54\ J + W\\W = -83.7\ J - 34.54\ J\\[/tex]

W = - 118.24 J (negative sign shows that work is done on piston)

Answer:

-49.2

Explanation:

Trust me bro

Answer:

v = 1247.92 m/s

Explanation:

The formula for kinetic energy is given as follows:

[tex]K.E = \frac{1}{2}mv^2[/tex]

Another formula that is used for Kinetic Energy is given as:

[tex]K.E = \frac{3}{2}KT[/tex]

Comparing both formulae for K.E:

[tex]\frac{1}{2}mv^2 = \frac{3}{2}KT\\\\mv^2 = 3KT\\v = \sqrt{ \frac{3KT}{m}}[/tex]

where,

v = rms speed of helium molecule = ?

K = Boltzmann Constant = 1.38 x 10⁻²³ J/k

T = Absolute Temperature = 250 K

m = mass of helium molecule = 6.646 x 10⁻²⁷ kg

Therefore,

[tex]v = \sqrt{\frac{(3)(1.38\ x\ 10^{-23}\ J/k)(250\ k)}{6.646\ x\ 10^{-27}\ kg}} \\\\[/tex]

v = 1247.92 m/s

Given that,

The rate of change of current = 3.2 A/s

Emf induced in the coil = 5.7 V

To find,

The magnitude of the mutual inductance of the two coils.

Solution,

The mutual inductance between the coils is given by the formula as follows :

[tex]\epsilon=M\dfrac{dI}{dt}\\\\M=\dfrac{\epsilon}{\dfrac{dI}{dt}}\\\\M=\dfrac{5.7}{3.2}\\\\=1.78\ H[/tex]

So, the mutual inductance of the two coils is 1.78 H.

Answer:

0 j

Explanation:

The work done by the employee on the box at the given zero displacement is 0 J.

The given parameters;

The work done by the employee on the box is calculated as follows;

W = Fd

where;

Since the employee sits on the box without moving it, the distance moved by the box = 0

W = 500 x 0

W = 0 J

Thus, the work done by the employee on the box is 0 J.

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Answer:

the answer may be mass and distance

Answer:

[tex]velocity(x)=15\,\frac{\pi}{4}\,cos(\frac{\pi}{4}x)[/tex]

Max speed = [tex]\frac{15\, \pi}{4} \,\, \frac{m}{s}[/tex]

Max acceleration = [tex]\frac{15\,\pi^2}{16} \,\,\frac{m}{s^2}[/tex]

Explanation:

Given the description of period and amplitude, the SHM could be described by:

[tex]f(x)=5\,sin(\frac{\pi}{4}x)[/tex]

and its angular velocity can be calculated doing the derivative:

[tex]f(x)=5\, \,sin(\frac{\pi}{4}x)\\f'(x)=5\,\frac{\pi}{4}\,cos(\frac{\pi}{4}x)[/tex]

And therefore, the tangential velocity is calculated by multiplying this expression times the radius of the movement (3 m):

[tex]velocity(x)=15\,\frac{\pi}{4}\,cos(\frac{\pi}{4}x)[/tex]  and is given in m/s.

Then the maximum speed is obtained when the cosine function becomes "1", and that gives:

Max speed = [tex]\frac{15\, \pi}{4} \,\, \frac{m}{s}[/tex]

The acceleration is found from the derivative of the velocity expression, and therefore given by:

[tex]acceleraton(x)=-15\,\frac{\pi^2}{16}\,sin(\frac{\pi}{4}x)[/tex]

and the maximum of the function will be obtained when the sine expression becomes "-1", which will render:

Max acceleration = [tex]\frac{15\,\pi^2}{16} \,\,\frac{m}{s^2}[/tex]

Answer:

A = 2 m from fulcrum

Explanation:

Product of anti clockwise  = Product of  clockwise moment

5 × 4 = 10 × A

20 = 10 x A

A = 20 / 10

A = 2 m from fulcrum

Answer:

48,2 m/s²

Explanation:

We're gonna use the Centripetal Acceleration formula: v² / r but before that, we got to know the velocity, that is not shown clearly to us, so....

To know the velocity let's calculate the distance that the ball traveled

The circumference of a circle formula is:

2piR

2 . 3,14 . 7,1 | That is equal to 44,588 m

We know that the ball traveled this distance 3,9 times, so...

44,588 . 3,9 = 173,8932 m

Ok, now we have the distance, just need to know the time, that is 9.4 seconds.

Velocity = Distance / Time

V = 173,8932 / 9,4

V = 18,5 (approximate)

So...

We are back to the first formula:

Ca = v² / r

Ca = 18,5² / 7.1

Ca = 48,2 m/s² (approximate)

I hope it is correct, hahaha.

Given that,

Mass of a sprinter = 70 kg

Initial velocity, u = 0

Final velocity, v = 10 m/s

Time, t = 3 s

To find,

Power output.

Solution,

The work done by the sprinter is equal to its kinetic energy.

[tex]W=\dfrac{1}{2}m(v^2-u^2)\\\\=\dfrac{1}{2}\times 70\times 10^2\\\\=3500\ J[/tex]

Let P is power output. Power is equal to work done per unit time. So,

[tex]P=\dfrac{3500\ J}{3\ s}\\\\=1166.67\ W[/tex]

So, the power output is 1166.66 W.

Answer:

1962 joules

Explanation:

m = 10 kg

h = 20 m

g = 9.81 ms^-2

PE = ?

PE = MGH

PE = 10 x 9.81 x 20

PE = 1962 joules

Answer:

B) Schizophrenia

Explanation:

Hope this helps!

Answer:

A, Magnetism

Explanation:

An ordinary electric generator produces electric power by spinning a strong magnet inside a set of wire coils. As the magnet spins, its magnetic field sweeps across the coils and gives rise to electric fields in those coils.

Hope this helps!!

Answer:

1.(c) 7

2.(d) 900

3.(b) two

4.(c) 0.0007

5.(d)0.0004

Explanation:

(1) White light after reflection through prism splits into 7 colors.

(2) Arabs and Chinese knew about lenses in about 900 AD

(3) There are Two more colors in the spectrum which cannot be seen with naked eye.

(4) Wavelength of red light is 0.0007mm

(5) Wavelength of violet light is 0.0004mm

Answer:

same for all objects

Explanation:

earth pulls every object by same force of gravity