Batteries have potential energy in their
energy stores. What one word completes the sentence?
​

Answer:

a. 7.38 N b. 40.87 N c. 0.113 kg-m²

Explanation:

Titan, Saturn's moon, has a thick atmosphere primarily composed of nitrogen. Its unique chemistry and thick atmosphere make it an interesting place for scientific study.

Titan, Saturn's moon, has a thick atmosphere made mostly of nitrogen. The atmosphere on Titan is thicker than Earth's and is primarily composed of nitrogen, with about 5% methane. The thick atmosphere and unique chemistry of Titan make it an interesting place for scientific study, as it may provide clues about the early chemistry of the solar system and the potential for life.

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A falling skydiver opens his parachute. A short time later, the weight of the skydiver-parachute system and the drag force exerted on the system are equal in magnitude. The following statements predicts the motion of the skydiver at this time

The skydiver is moving downward with constant speed.

Explanation:

Immediately on leaving the aircraft, the skydiver accelerates downwards due to the force of gravity. There is no air resistance acting in the upwards direction, and there is a resultant force acting downwards. The skydiver accelerates towards the ground.

The forces acting on a falling leaf are : gravity and air resistance.

The net force and the acceleration on the falling skydiver is upward.

An upward net force on a downward falling object would cause that object to slow down. The skydiver thus slows down.

As the speed decreases, the amount of air resistance also decreases until once more the skydiver reaches a terminal velocity.

A skydiver falling at a constant speed opens his parachute. When the skydiver is falling, the forces are unbalanced.

The drag force opposes the relative motion of an object in a fluid

The option that gives the statement that predicts the motion of the skydiver when the magnitude of the weight of the skydiver-parachute system and the drag force are equal is option b.

b. The skydiver is moving downward with constant speed

The reason the above option is correct is as follows:

The skydiver is falling through the air which is a fluid and is therefore subject to drag force, [tex]F_D[/tex], which is given as follows;

[tex]F_D = \dfrac{1}{2} \times \rho \times v^2 \times C_D \times A[/tex]

Where;

[tex]F_D[/tex] = The drag force

ρ = The fluid density

v = The relative object speed compared to the fluid

A = Cross sectional area

[tex]C_D[/tex] = The drag coefficient

Therefore, given that the surface area of the falling skydiver is largely increased when the parachute is opened and the drag force is a function of the square of the velocity, we have that the drag force rapidly equals the weight of the skydiver, such that the net force becomes zero, and therefore, the speed of the skydiver becomes constant

Therefore, the correct option is that the skydiver is moving downward with constant speed

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The coefficient of linear expansion for the material of the rod can be calculated using the formula ΔL/L = α ΔT to be α = 2 x 10⁻⁵ °C⁻¹.

The subject of this question is the calculation of the coefficient of linear expansion for a certain material. The relevant formula here is: ΔL/L = α ΔT, where ΔL is change in length, L is original length, α is coefficient of linear expansion and ΔT is change in temperature.

Firstly, we calculate the change in length of the rod (ΔL) which is the final length minus initial length, 20.11 cm - 20.05 cm = 0.06 cm. Then, the change in temperature (ΔT) is the final temperature minus the initial one: 270°C - 20°C = 250°C.

After substitution into the formula, we get 0.06 cm / 20.05 cm = α × 250°C. Solving for α, we get the coefficient of linear expansion for the material of the rod to be α = 2 x 10-5 °C⁻¹.

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The coefficient of linear expansion for the material of the rod is approximately 0.011974 cm/°C.

To find the coefficient of linear expansion for the material of which the rod is made, we can use the equation for linear thermal expansion:

ΔL = αLΔT

where ΔL is the change in length, α is the coefficient of linear expansion, L is the initial length of the rod, and ΔT is the change in temperature.

Given that the initial length of the rod is 20.05 cm, the final length is 20.11 cm, and the change in temperature is 270 °C - 20 °C = 250 °C, we can substitute these values into the equation to solve for α:

Hence, the coefficient of linear expansion for the material of which the rod is made is approximately 0.011974 cm/°C.

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Answer:

Picture C

Explanation:

Answer: find the attached figure for a and b

Explanation:

A) The second figure depict electric field lines and equipotential lines for two equal but opposite charges. The equipotential lines can be drawn by making them perpendicular to the electric field lines. The potential is greatest (most positive) near the positive charge and least (most negative) near the negative charge.

B) The figure attached depicts an isolated point charge Q with its electric field lines in blue and equipotential lines in green. The potential is the same along each equipotential line, meaning that no work is required to move a charge anywhere along one of those lines. Work is needed to move a charge from one equipotential line to another. Equipotential lines are perpendicular to electric field lines in every case.

Please find the attached file for the figure

Explanation:

Given that,

(a) Frequency, [tex]f_1=4\times 10^{19}\ Hz[/tex]

All electromagnetic wave moves with the speed of light. It is given by :

[tex]c=f\lambda[/tex]

[tex]\lambda_1=\dfrac{c}{f_1}\\\\\lambda_1=\dfrac{3\times 10^8}{4\times 10^{19}}\\\\\lambda_1=7.5\times 10^{-12}[/tex]

(b) Frequency, [tex]f_2=5.5\times 10^{1=9}\ Hz[/tex]

All electromagnetic wave moves with the speed of light. It is given by :

[tex]c=f\lambda[/tex]

[tex]\lambda_2=\dfrac{c}{f_2}\\\\\lambda_2=\dfrac{3\times 10^8}{5.5\times 10^{9}}\\\\\lambda_2=0.054\ m[/tex]

Hence, this is the required solution.

Answer:

The torque applied by the drill bit is T = 16.2 Nm and the cutting force of the drill bit is F = 33 N.

Explanation:

Given:-

- The diameter of the drill bit, d = 98 cm

- The power at which drill works, P = 5.85 hp

- The rotational speed of drill, N = 1900 rpm

Find:-

What Torque And Force Is Applied To The Drill Bit?

Solution:-

- The amount of torque (T) generated at the periphery of the cutting edges of the drilling bit when it is driven at a power of (P) horsepower at some rotational speed (N).

- The relation between these quantities is given:

                         T = 5252*P / N

                         T = 5252*5.85 / 1900

                         T = 16.171 Nm

- The force (F) applied at the periphery of the drill bit cutting edge at a distance of radius from the center of drill bit can be determined from the definition of Torque (T) being a cross product of the Force (F) and a moment arm (r):

                          T = F*r

Where,   r = d / 2

                          F = 2T / d

                          F = 2*16.171 / 0.98

                          F = 33 N

Answer: The torque applied by the drill bit is T = 16.2 Nm and the cutting force of the drill bit is F = 33 N.

Answer:

1) Torque = 21.934 Nm

2) force = 44.76 N

Explanation:

Power = 5.88 hp

1 hp = 746 W

Power = 5.88 x 746 = 4364.1 W

Angular speed in Rpm = 1900 rpm

But angular speed w = (2¶N)/60 rad/s

= (2 x 3.142 x 1900)/60 = 198.968 rad/s

From,

1) Power P = T x w

Where T = torque

T = P/W = 4364.1/198.968 = 21.934 Nm

2) diameter of drill = 98 cm

Radius = 98/2 = 49 cm = 49x10^-2 m

From torque T = Force x radius

Force = Torque /radius

F = 21.934/49x10^-2 = 44.76 N

The electromagnetic waves from the lowest frequency to the highest frequency are gamma rays, X-ray, visible light, and infrared.

Electromagnetic waves are the waves which are formed when an electric field couples with a magnetic field. Magnetic and the electric fields of an electromagnetic wave are perpendicular to each other and to the direction of the wave propagation. Electromagnetic waves are used widely in the food processing for destroying microbes.

Therefore, the correct order of electromagnetic waves from the lowest frequency to the highest frequency are gamma rays, X-ray, visible light, and infrared.

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Answer:

[tex]T(1)=21 [/tex]

Explanation:

The equation of the position in kinematics is given:

[tex]x(t)=x_{0}+v_{0}t+0.5at^{2}[/tex]

So the equation will be:

[tex]x(t)=20t+0.5*2*t^{2}[/tex]

[tex]x(t)=20t+t^{2}[/tex]    

Now, the Taylor polynomial equation is:

[tex]f(a)+\frac{f'(a)}{1!}(x-a)+\frac{f''(a)}{2!}(x-a)^{2}+...[/tex]

Using our position equation we can find f'(t)=v(t) and f''(x)=a(t). In our case a=0, so let's find each derivative.

[tex]f(t)=x(t)=20t+t^{2}[/tex]

[tex]f'(t)=\frac{dx(t)}{dt}=v(t)=20+2t[/tex]

[tex]f''(t)=\frac{dv(t)}{dt}=a(t)=2[/tex]

Using the Taylor polynomial with a = 0 and take just the second order of the derivative.

[tex]f(0)+\frac{f'(0)}{1!}(x)+\frac{f''(0)}{2!}(x)^{2}[/tex]

[tex]f(0)=x(0)=0[/tex]

[tex]f'(0)=v(0)=20[/tex]

[tex]f''(0)=a(0)=2[/tex]

[tex]T(t)=f(0)+\frac{f'(0)}{1!}(t)+\frac{f''(0)}{2!}(t)^{2}[/tex]

[tex]T(t)=\frac{20}{1!}(t)+\frac{2}{2!}(t)^{2}[/tex]

[tex]T(t)=20t+t^{2}[/tex]

Let's put t=1 so find the how far the car moves in the next second:

[tex]T(1)=20*1+1^{2}[/tex]

[tex]T(1)=21 [/tex]

Therefore, the position in the next second is 21 m.

We need to know if the acceleration remains at this value to use this polynomial in the next minute, so I suggest that it would be reasonable to use this method just under this condition.

I hope it helps you!

The magnitude of the net magnetic field at the common center can be calculated using the formula MOI B = (at the center of the loop)/2R. The magnetic field strength at the center is approximately 6.28 × 10-5 T.

The magnitude of the net magnetic field at the common center can be calculated using the formula for the magnetic field strength at the center of a circular loop, which is given by MOI B = (at the center of the loop), 2R. In this case, the radius of each loop is 5.00 cm. Plugging in the values, the magnetic field strength at the center can be calculated.

Substituting the given values into the equation:

Magnetic field strength = MOI B = (2 × π × (5.00 cm)²)(2.10 A)/(2 × 5.00 cm) ≈ 6.28 × 10-5 T

Therefore, the magnitude of the net magnetic field at the common center is approximately 6.28 × 10-5 T.

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The net magnetic field at the common center of the loops will be 3.71 × 10⁻⁵ T.

The two circular loop of wire have their planes perpendicular to each other and share a common centre. This indicates that the direction of net magnetic field at the common centre due to any one of the loops will be perpendicular to the direction of the net magnetic field at the common centre due to the other loop.

As both the loops have the same radius (r), same number of turns (N), and carry the same current (I), hence, the magnetic field at the centre of the loops will have the same magnitude and can be given by the formula:

[tex]B = \frac{N\mu_oI}{2r}[/tex]

Given that:

N = 1

I = 2.10 A

r = 5.00 cm = 0.05 m

μ₀ = 4π × 10⁻⁷

Substituting the values, we get:

[tex]B = \frac{(4 \pi \times 10^{-7})(2.10 A)}{2(0.05 m)}[/tex]

B = 2.63 × 10⁻⁵ T

The net magnetic field at the common centre can be found using

[tex]B_{net} = \sqrt{B_1^{2} +B_2^{2} +2B_1B_2cos\theta}[/tex]

as both the magnetic fields are perpendicular to each other the angle (θ) between them will be 90°.

∴ [tex]B_{net} = \sqrt{B_1^{2} +B_2^{2} }[/tex]

[tex]B_{net} = \sqrt{2B^{2} }[/tex]

[tex]B_{net} = \sqrt{2(2.63 \times 10^{-5} T)^{2} }[/tex]

[tex]B_{net} = (2.63 \times 10^{-5} T)\sqrt{2} }[/tex]

or, [tex]B_{net} = 3.71 \times 10^{-5} \hspace{0.5mm} T[/tex]

Answer:

From smallest ratio to the largest ratio:

Coasting Universe - Critical Universe - Recollapsing Universe(From left to right)

Explanation:

The coasting universe is one that expands at a constant rate given by the Hubble constant throughout all of cosmic time. It has a ratio of actual density to critical density that is less than 1

The critical universe is one that is at balance with no expansion .I.e. the actual density and the critical density are equal, which makes the ratio of actual density to critical density to be equal to 1

Recollapsing Universe: The expansion of the universe reverses in the future and the universe eventually recollapses. The recollapsing universe has the ratio of the actual density to the critical density to be greater than 1

From smallest to largest ratio of actual mass density to critical density, the models are: coasting universe, critical universe, and recollapsing universe. In a coasting universe, expansion continues at a decreasing rate. A critical universe's expansion slows to an eventual stop. A recollapsing universe's expansion ultimately reverses, leading to contraction.

The long-term expansion and possible contraction of the universe under different scenarios or models, in the absence of dark energy, can be ranked based on the ratio of its actual mass density to the critical density.

Continuing from the smallest mass density ratio to the largest, it would be: the coasting universe, the critical universe, and finally the recollapsing universe.

In a coasting universe, the actual density is lower than the critical density. Thus, it would continue to expand forever but at a decreasing rate. In a critical universe, the actual density equals the critical density, which means the universe's expansion will gradually slow to a stop in an infinitely far future. Lastly, in a recollapsing universe, the actual density is greater than the critical density. This leads to an eventual reversal of the expansion, causing the universe to start contracting.

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Answer:

Commutator.

Explanation:

It is electrical switch and consist of cylinder. Split rings are two halves of a ring that act as a Commutator. When current in the coil is Zero and is about to change the direction.

a.  The greatest angle will be bouncing, then embedded and finally the least is passing angle.

b. The  Momentum is greatest when the arrow bounces and least when the arrow passes.  This justify the obtained ranking of angles.

The given problem is based on the concept of momentum and angle made at various instance. Momentum is defined as an impact caused due to applied force. It is expressed as the product of mass and velocity of an object, with respect to the direction. Taking forward direction of arrow as positive then backward direction will be negative.

From the law of conservation of linear momentum, the sum of initial and final momentum should be equal.

Thus we can conclude that by ranking the angles, consider that the maximum angle that the pumpkin reaches depends on the speed of the pumpkin. The greatest angle will be bouncing, then embedded and finally the least is passing angle.

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Answer:

an electronic symbol is a pictogram used to represent various electrical and electronic devices or functions such as wires batteries resistors and transistors in a symptomatic diagram of an electrical or electronic circuit.

Explanation:

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Final answer:

Electrical circuit diagrams use specific standardized symbols to represent various components like wires, batteries, resistors, ground, and capacitors. Symbols for wire, resistor, and battery are straightforward, while capacitors have variations depending on type. ANSI and IEC provide different standard symbol guidelines.

Explanation:

Symbols for Components of Electrical Circuits

Electrical circuit diagrams use standardized symbols to represent different components. The wire is depicted as a thin black line and is assumed to be a perfect conductor in diagrams, although in reality it is not perfect but typically close enough for practical purposes. A battery or voltage source is represented by a set of parallel lines, with the longer line denoting the positive terminal and the shorter line the negative terminal. The resistor is illustrated with a zigzag symbol, which includes any resistance within the circuit connections. Ground is typically shown as a set of one to three horizontal lines, sometimes with one of the lines angled towards the bottom.

When it comes to alternating current (AC) sources, the symbol is a sine wave enclosed in a circle. This shows the oscillating nature of the AC voltage. Capacitors are represented with two parallel lines for a fixed capacitor; an electrolytic capacitor is shown with one curved line indicating the negative terminal and one straight line for the positive terminal. A variable-capacitance capacitor is represented with an arrow through the parallel lines, signifying adjustability.

Standards such as the American National Standard Institute (ANSI) and the International Electrotechnical Commission (IEC) provide guidelines for these symbols. While the ANSI standard is widely used for its recognizability, the IEC standard might be preferred for more complex circuits due to its cleaner presentation.

Answer: plate tectonics

Explanation: plate tectonics move constantly movement in narrow zones along plate boundaries causes earthquakes and plate tectonics come together and create pressure upon the magma deposit underground forcing it up into a volcanic eruption

Answer:

the magnitude of the torque about the point where the beam is bolted into place 12.32kNm

Explanation:

N/B The units given in the question are meant to be m, kg and kg respectively

Given data

Length of beam 3.7m

Mass of beam 520kg

Mass of construction worker 73kg

Torque is expressed as the moment or turning effect brought about by a couple

T= F*d

Where d=perpendicular distance

F= force

Converting The mass of the beam and the worker to force we have

520*10= 5200N

73*10=730N

Note that the force due to the mass of the beam is acting at the center of the beam

See the free body diagram attached

Taking moments about point O

Torque =Σ Fxd

Torque =5200x1.85+7x3.7

=9620+2701

=12321 Nm

=12.32kNm

Answer:

cop = 4.859

power = 30.87 KW

Explanation:

the pictures attached herewith shows the calculation

By calculating the work input to the compressor (Wc) using the COP formula and known cooling load (Qc), and assuming a COP of 4, the power required is 37.5 kW.

To determine the Coefficient of Performance (COP) and power required for the ideal vapor-compression refrigeration cycle, we'll use the following steps and equations:

Find the Heat Transfer in the Evaporator (Qc):

Given Cooling Load (Qc) = 150 kW.

Calculate Work Input to the Compressor (Wc):

Using the first law of thermodynamics:

Qc = Wc + Qh

Rearrange to find Wc:

Wc = Qc - Qh

Determine Heat Rejected in the Condenser (Qh):

To find Qh, we need to calculate the change in enthalpy in the evaporator and condenser using refrigerant properties, such as specific enthalpy values. For refrigerant R-134a at -12 degrees Celsius, you can use property tables or software to find the enthalpy values.

Find COP:

COP is defined as:

COP = Qc / Wc

Calculate Power Required for Service:

Using the COP and Qc:

Wc = Qc / COP

Now, let's calculate:

Assuming a COP value (e.g., 4):

Wc = 150 kW / 4 = 37.5 kW

So, with a chosen COP of 4, the power required for the service is 37.5 kW.

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Answer:

In the lab activity, I used a virtual watershed to demonstrate how pollutants enter and flow through the watershed. I constructed food chains to show how biotic factors are related. I also predicted and modeled how human activity affected the biotic factors in an ecosystem. Based on my observations, I can conclude that biotic and abiotic factors are closely linked and that human activity that changes the environment, like pollution, can affect all the other parts of an ecosystem in a negative way.

Explanation:

Answer:

In the lab activity, I used a virtual watershed to demonstrate how pollutants enter and flow through the watershed. I constructed food chains to show how biotic factors are related. I also predicted and modeled how human activity affected the biotic factors in an ecosystem. Based on my observations, I can conclude that biotic and abiotic factors are closely linked and that human activity that changes the environment, like pollution, can affect all the other parts of an ecosystem in a negative way.

Answer:

d) The image would be dimmer

Explanation:

When inverted image of an object is viewed on a screen from the side facing a converging lens, the

lens focuses the diverging, and blurred light rays from the distance object through refraction of the rays two times.Then the rays is converge by the double bending cl at a focal point behind the lens inorder for a sharper image to be be observed.

But when an opaque card is then introduced to cover only the upper half of the lens then the image becomes dimmer because of the reduction in the light intensity on the screen by 50%

When the opaque card should be introduced so here the image should be considered as the dimmer.

At the time when the inverted image should be viewed on the screen that faced the converging lens so here the lens should be focused on the diverging also there should be blurred light rays from the distance object via the refraction of the rays.

However, at the time there is the opaque card so here the image should be dimmer since there is the decrease in the light intensity by 50%/

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Answer:

The flow area at the location where the Mach number is 0.9 is 25.24 cm²

Explanation:

Here we have for isentropic flow;

[tex]\frac{A}{A^*} = \frac{1}{M}(\frac{2}{k+1} (1+\frac{k-1}{2}M^2))^{(\frac{k+1}{2(k-1)} )[/tex]

Where:

A = Area of flow = 36 cm²

M = Mach number at section of = 1.8

k = Specific heat ratio = 1.4

A* = Area at the throat

Therefore, plugging the values we get

[tex]\frac{36}{A^*} = \frac{1}{1.8}(\frac{2}{1.4+1} (1+\frac{1.4-1}{2}1.8^2))^{(\frac{1.4+1}{2(1.4-1)} ) = 1.439[/tex]

Therefore, A* = 36/1.439 = 25.01769 cm²

Where the Mach number is 0.9, we have

[tex]\frac{A}{25.02} = \frac{1}{0.9}(\frac{2}{1.4+1} (1+\frac{1.4-1}{2}0.9^2))^{(\frac{1.4+1}{2(1.4-1)} ) = 1.009[/tex]

Therefore A = 25.020× 1.009 = 25.24 cm²

The flow area at the location where the Mach number is 0.9 = 25.24 cm².

Answer:

300 minutes.

Explanation:

Given,

Speed of car 1 = 60 Km/h

Speed of car 2 = 75 Km/h

distance travel by car 2 to catch car 1 = 75 Km

time taken to catch the car = ?

Relative velocity between the car = 75 - 60 = 15 Km/h

[tex]time = \dfrac{distance}{speed}[/tex]

[tex]time = \dfrac{75}{15}[/tex]

t = 5 hrs

t = 5 x 60 = 300 minutes.

Two cars passing a point at different speeds can be calculated using time, distance, and speed formulas.

A car passes the Eiffel Tower driving at a constant rate of 60 km per hour. A second car, traveling at a constant rate of 75 km per hour, passes the Eiffel Tower later and catches the first car after traveling 75 km past the tower.

To calculate the time difference between the two cars passing the Eiffel Tower, we can use the formula: Time = Distance / Speed. The second car passes the tower 15 minutes after the first car.

Answer:

Kinetic energy of the car = 4637.04 J

Explanation:

Mass of the car (m) =1200 kg

speed of the car (v) = 2.78 m/sec

Kinetic energy =[tex]\frac{1}{2}mv^{2}[/tex]

Putting the values of m and v,

Hence, Kinetic Energy of the car =[tex]\frac{1}{2}1200\cdot 2.78^{2}[/tex] =  4637.04 J

The kinetic energy of a 1,200kg car traveling at a speed of 2.78 m/s is calculated using the formula KE = ½ mv², yielding a kinetic energy of 4,634.88 joules.

To calculate the kinetic energy (KE) of a car with a mass of 1,200kg traveling at a speed of 2.78 m/s, we need to use the kinetic energy formula KE = ½ mv². Plugging in the given values, we have:

KE = ½ (1,200 kg) × (2.78 m/s)²

KE = ½ × 1,200 kg × 7.7284 m²/s²

KE = 4,634.88 J

Therefore, the kinetic energy of the car is calculated to be 4,634.88 joules.

Answer:

Velocity after collision will be 5.56 m/sec

So option (a) will be correct answer

Explanation:

Mass of steel ball [tex]m_1=200gram=0.2kg[/tex]

Speed of steel ball before collision [tex]v_1=25m/sec[/tex]

Mass of large ball [tex]m_2=700gram=0.7kg[/tex]

Velocity of large ball [tex]v_2=0m/sec[/tex]

According to conservation of momentum

[tex]m_1v_1+m_2v_2=(m_1+m_2)v[/tex]

[tex]0.2\times 25+0.7\times 0=(0.7+0.2)v[/tex]

[tex]v=5.56m/sec[/tex]

So velocity after collision will be 5.56 m/sec

So option (a) will be correct answer

Answer:

D) Einstein proved it is impossible to have a redshift greater than 1; these are all due to gravitational lensing tricking us

Explanation:

By Einstein's theory of relativity the maximum value of the red shift is 1. This correspond to a case in which the observed frequency equals the emitted frequency:

[tex]z=\frac{f_e-f_o}{f_o}[/tex]

in other cases the red shift is lower than one.

Hence, the gravitational lens change the measurements of the observed frequency and because of that we calculate a greater red shift.

Hence, the answer is:

D) Einstein proved it is impossible to have a redshift greater than 1; these are all due to gravitational lensing tricking us

hope this helps!!

Answer:

time taken to reach maximum height(t)=3seconds

Explanation:

1st equation of motion:v=u-gt ,but v=0 at maximum height.so 0=u-gt

t=u÷g where,u=30m/s,h=20m,g=10m/s square

so t=30÷10

t=3seconds

Answer:

The answer to your question is given below

Explanation:

Since both object A and B were dropped from the same height and the air resistance is negligible, both object A and B will get to the ground at the same time.

From the question, we were told that object A falls through a distance to dA at time t and object B falls through a distance of dB at time 2t.

Remember, both objects must get to the ground at the same time..!

Let the time taken for both objects to get to the ground be t.

Time A = Time B = t

But B falls through time 2t

Therefore,

Time A = Time B = 2t

Height = 1/2gt^2

For A:

Time = 2t

dA = 1/2 x g x (2t)^2

dA = 1/2g x 4t^2

For B

Time = t

dB = 1/2 x g x t^2

Equating dA and dB

dA = dB

1/2g x 4t^2 = 1/2 x g x t^2

Cancel out 1/2, g and t^2

4 = 1

4dA = dB

Divide both side by 4

dA = 1/4 dB

Answer:

Centripetal force, F = 66.36 N

Explanation:

Given that,

Mass of the monkey, m = 8.72 kg

The radial distance between the branch and the point where the monkey's mass is located to be 84.1 cm, r = 84.1 cm

The speed of the monkey, v = 2.53 m/s

We need to find the  magnitude of the centripetal force acting on the monkey. It is given by :

[tex]F=\dfrac{mv^2}{r}\\\\F=\dfrac{8.72\times (2.53)^2}{84.1\times 10^{-2}}\\\\F=66.36\ N[/tex]

So, the magnitude of the centripetal force acting on the monkey is 66.36 N.