8. How did the measured angular magnification of the telescope compare with the theoretical prediction?

Answer:

y becomes doubled.

Explanation:

If;

       y  = \(\frac{k}{x}\)  

what is the state of y when x is halved;

  the given expression is an inverse relationship. When y increases, x is supposed to decrease and vice versa.

 if x is halved; x  = \(\frac{x}{2}\)

           \(\frac{k}{\frac{x}{2} }\)   = \(\frac{2k}{x}\)  

Now compare :

      \(\frac{k}{x}\)  :  \(\frac{2k}{x}\)

we see that y becomes doubled

Okay, here are the steps to calculate the full distance traveled when an object is thrown at a certain speed and angle:

You have the initial velocity (v): 35 m/s

You have the launch angle (θ): 45 degrees

We need to split the initial velocity into its horizontal (vx) and vertical (vy) components.

To calculate vx (horizontal component):

vx = v * cosθ

vx = 35 * cos(45) = 24.7 m/s

To calculate vy (vertical component):

vy = v * sinθ

vy = 35 * sin(45) = 24.7 m/s

We can calculate the horizontal distance (d) traveled using:

d = vx * t (where t is time)

Since there is no air resistance, the vertical velocity (vy) will remain constant. This means the time the object is in the air is:

t = vy / g (where g is acceleration due to gravity, 9.8 m/s^2)

t = 24.7 / 9.8 = 2.52 seconds

Now we can calculate the full horizontal distance traveled:

d = vx * t

d = 24.7 * 2.52

= 62.3 meters

So the full distance the object will travel when thrown at 35 m/s at a 45 degree angle is approximately 62 meters.

Let me know if you have any other questions!

Answer:

To calculate the full distance traveled by an object thrown at a velocity of 35 m/s at an angle of 45 degrees, we need to consider the horizontal and vertical components of the motion separately.

The horizontal component of the motion remains constant throughout the trajectory and is given by:

Horizontal distance = (Initial velocity) * (Time of flight) * cos(angle)

In this case, the initial velocity is 35 m/s, the angle is 45 degrees, and we need to find the time of flight.

The time of flight can be calculated using the vertical component of the motion. The vertical motion can be described using the equation:

Vertical displacement = (Initial velocity * sin(angle))^2 / (2 * acceleration)

Where the initial velocity is 35 m/s, the angle is 45 degrees, and the acceleration is the acceleration due to gravity, approximately 9.8 m/s^2.

The vertical displacement is zero at the highest point of the trajectory since the object comes back down to the same height it was launched from. So we can solve the equation for the time of flight.

Using these calculations, we can find the horizontal distance traveled by the object.

Let's calculate step by step:

Step 1: Calculate the time of flight

Vertical displacement = 0 (at the highest point)

0 = (35 * sin(45))^2 / (2 * 9.8)

0 = (24.75^2) / 19.6

0 = 616.0125 / 19.6

0 = 31.43

Step 2: Calculate the time of flight

Vertical displacement = (Initial velocity * sin(angle)) * time - (1/2) * acceleration * time^2

0 = (35 * sin(45)) * time - (1/2) * 9.8 * time^2

0 = 24.75 * time - 4.9 * time^2

4.9 * time^2 - 24.75 * time = 0

time * (4.9 * time - 24.75) = 0

time = 0 (initial point) or 24.75 / 4.9

time = 5.05 seconds

Step 3: Calculate the horizontal distance

Horizontal distance = (Initial velocity) * (Time of flight) * cos(angle)

Horizontal distance = 35 * 5.05 * cos(45)

Horizontal distance = 35 * 5.05 * (sqrt(2)/2)

Horizontal distance = 88.96 meters

Explanation:

the sum of two or more vector is resultant vector.

Answer:

vb = 298 m/s

Explanation:

Given:-

- The mass of the bullet, mb = 5.00 g

- The mass of the wooden block, mw = 1.2 kg

- The coefficient of kinetic friction between block and horizontal surface, \(u_k = 0.2\)

- The bullet and block combined moves a distance after impact, s = 0.390

Solution:-

- We will first consider the motion of the block and bullet combined after the bullet is embedded into the block.

- We are told that the wooden block is rested on a horizontal floor with coefficient of kinetic friction ( uk ).

- When the bullet is embedded into the block. Both combined will move with a velocity ( V ). Both will eventually loose all of their kinetic energy by doing work against the friction.

- We will apply the work - energy principle to the system ( block + bullet ) as follows:

                                \(W = dE_k\)

Where,

                W: Work done against friction

                dEk: The change in kinetic energy of the system

- The work-done against friction is the product of frictional force ( Ff ) and the displacement over which the system travels ( s ).

- The frictional force  ( Ff ) is proportional to the contact force ( N ) between the system and the surface.

- Apply static balance on the system in the direction normal to the surface as follows:

                              \(N - ( m_b + m_w )*g = 0\\\\N = ( m_b + m_w )*g\)

- The frictional force is defined as:

                              \(F_f = u_k*N\\\\F_f = u_k* ( m_b + m_w ) * g\)

- The work done against friction ( W ) is defined as:

                              \(W = F_f*s\\\\W = u_k*(m_b + m_w )*g*s\)

Where,

                         g: the gravitational acceleration constant = 9.81 m/s^2

- Now use the energy balance to determine the velocity of the system after impact ( V ):

                          \(u_k*( m_b + m_w )*g*s = 0.5*( m_b + m_w )*V^2\\\\V = \sqrt{2*u_k*g*s } \\\\V = \sqrt{2*0.2*9.81*0.39 }\\\\V = 1.23707 m/s\)

- Now we will again consider an independent system of bullet and the wooden block resting on the horizontal surface.

- The bullet is fired with velocity ( vb ) towards the wooden block. The system can be considered to be isolated and all other fictitious effects can be ignored. This validates the use of conservation of linear momentum for this system.

- The conservation of linear momentum denotes:

                          \(P_i = P_f\)  

Where,

                 Pi: the inital momentum of the system

                 Pf: the final momentum of the system

- Initially the block was at rest and bullet had a velocity ( vb ) and after striking the bullet is embedded into the block and moves with a velocity ( V ).

                      \(m_b*v_b = ( m_b + m_w )*V\\\\v_b = \frac{ ( m_b + m_w )}{m_b}*V\\\\v_b = \frac{ ( 0.005 + 1.2 )}{0.005}*(1.23707)\\\\v_b = 298 m/s\)

Answer: The initial speed of the bullet is equivalent to the speed of the bullet just before the impact as vb = 298 m/s. This is under the assumption that forces like ( air resistance or gravitational or impulse) have negligible effect.

The mass of the Ball B is 1.35 x 10⁻⁶ kg.

Gravitational Force is described by Newton's law of universal gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The law of universal gravitation is important in many fields, including astronomy, physics, and engineering.

The gravitational force F between two objects of masses m1 and m2 separated by a distance r is given by:

F = G(m₁m₂)/r²

where G is the gravitational constant.

We can rearrange the equation to solve for the mass of Ball B:

m₂ = Fr²/Gm₁

Substituting the given values, we get:

m₂ = (8.7 x 10⁻¹⁰ N)(3.0 m)²/(6.6743 x 10¹¹ N(m^2/kg²))(30 N)

m₂ = 1.35 x 10⁻⁶ kg

Therefore, the mass of Ball B is approximately 1.35 x 10⁻⁶kg.

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(B) 1.58×10³ V

Explanation:

If you divide the input voltage by the number of turns in the primary coil, the result will be equal to the output voltage divided by the number of turns in the secondary coil:

Ui/Np = Uo/Ns

83/250 = Uo/4750 multiply both sides by 4750

394250/250 = Uo

Uo = 1577 = 1.58×10³ V

Answer:

The furnace has a temperature of 585 degrees Celsius.

Temperature is an expression denoting hotness or coolness on any scale, including Fahrenheit and Celsius. According to temperature, heat energy will naturally move from a hotter (body with a higher temperature) to a colder (body with a lower temperature) (one at a lower temperature).

Agriculture, food production, and medical care—for both humans and animals—all rely largely on

The centripetal force in Newtons provided by the friction between the blade of the skate and the ice is 490 N

The following data were obtained from the question:

The centripetal force can be obtained as illustrated below:

F = mv²/r

= (50 × 7²) / 5

= (50 × 49) / 5

= 2450 / 5

= 490 N

Thus, we can concluded that the centripetal force is 490 N

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The statement that describes the transformation of the graph of function f onto the graph of function g is: The graph shifts 2 units right and 7 units down.

To determine the transformation of the graph of function f onto the graph of function g, we compare the two functions f(x) and g(x) and observe the changes in the equations.

The function f(x) = (1/x - 3) + 1 represents a reciprocal function that is shifted vertically 1 unit up and horizontally 3 units to the right. The reciprocal function is reflected about the line y = x.

The function g(x) = (1/(1 + 4)) + 3 simplifies to g(x) = 4 + 3 = 7, which is a constant function representing a horizontal line at y = 7.

By comparing the equations, we can see that the transformation from f(x) to g(x) involves the following changes:

The term 1/x in f(x) is replaced by the constant 1/(1 + 4) in g(x), resulting in a vertical shift of 7 units up.

The term -3 in f(x) is replaced by 3 in g(x), resulting in a vertical shift of 3 units up.

The +1 in f(x) is replaced by +3 in g(x), resulting in an additional vertical shift of 2 units up.

Therefore, the overall transformation is a shift of 2 units to the right and 7 units down.

Hence, the correct statement is: The graph shifts 2 units right and 7 units down.

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Answer:

The strength of the source charge's electric field could be measured by any other charge placed somewhere in its surroundings. The charge that is used to measure the electric field strength is referred to as a test charge since it is used to test the field strength. The test charge has a quantity of charge denoted by the symbol q.

Explanation:

Electric field strength is a vector quantity; it has both magnitude and direction. The magnitude of the electric field strength is defined in terms of how it is measured. Let's suppose that an electric charge can be denoted by the symbol Q. This electric charge creates an electric field; since Q is the source of the electric field, we will refer to it as the source charge. The strength of the source charge's electric field could be measured by any other charge placed somewhere in its surroundings. The charge that is used to measure the electric field strength is referred to as a test charge since it is used to test the field strength. The test charge has a quantity of charge denoted by the symbol q. When placed within the electric field, the test charge will experience an electric force - either attractive or repulsive. As is usually the case, this force will be denoted by the symbol F. The magnitude of the electric field is simply defined as the force per charge on the test charge.

Answer:

C .energy from the sun, carbon dioxide in the air, water

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The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.

The p-waves travel with a constant velocity of 7 km/s

The time can be calculated by using the formula

t = d / v

where

T1 =  10:05 a.m

d is the distance they take to travel from the epicenter

v is the speed of the p-waves

On average, the speed of p-waves is

v = 7 km/s

d = 5600 km (given)

Substituting the values in the formula;

t = d / v

t = 5600 ÷ 7

t = 800 seconds

Converting into minutes,

t = 800 ÷ 60

t = 13.3

≈ 13 mins

T1 -  13 mins = T2

10:05 - 13 mins = 9.52 am

It means the earthquake occurred prior 13 minutes, that is at 9.52 am.

Therefore, the earthquake occurred at 9.52 am.

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a) A microwave oven that draws 0.8 kWh is used for one hour. At a cost of 7.5 cents per kWh, then the cost of the microwave’s electrical energy consumption is 7.5 cents per kWh.

b) the cost for the microwave if it is used one day for 20 min is  1.98 cents.

(c) the cost of using the microwave for 20 min a day for a month of 30 days is 59.4 cents.

Given,

Energy consumption of microwave = 0.8 kWh

cost = 7.5 cents/kWh

20 min = 0.33hr

Energy consumption in 20 min = 0.8 kWh × 0.33 = 0.26 kWh.

cost for 20= 0.26 kWh × 7.5 cents/kWh = 1.98 cents

cost for 30 days,

1.98 cents × 30 days = 59.4 cents.

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The magnitude of the displacement vector refers to the length or amount of the displacement vector. Displacement is the change in position of an object. Displacement is a vector quantity, which means it has both magnitude and direction. In this question, a figure skater is gliding along a circular path of radius 3.93 m.

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Answer:

75 cm/second.

Explanation:

Formula:

Walking speed = stride length / time per step

Walking speed = 90cm/time per step

                         = 90cm/1.2 seconds (a common estimate time per step)

                         = 75cm/second.

Answer:

:To find the Voltage, ( V ) [ V = I x R ] V (volts) = I (amps) x R (Ω)

To find the Current, ( I ) [ I = V ÷ R ] I (amps) = V (volts) ÷ R (Ω)

To find the Resistance, ( R ) [ R = V ÷ I ] R (Ω) = V (volts) ÷ I (amps)

To find the Power (P) [ P = V x I ] P (watts) = V (volts) x I (amps)

Answer:

1. t = 5.89 s

2. h = 170 m

3. Vf = 57.8 m/s

Explanation:

1.

First, we analyze the horizontal motion of the golf ball. Assuming the air friction to be negligible, the horizontal motion will be uniform. So, e can use the following equation:

\(s = vt\)

where,

s = horizontal distance covered by the golf ball = 471 m

v = horizontal speed of golf ball = 80 m/s

t = time taken by the golf ball in air = ?

Therefore,

\(471\ m = (80\ m/s)t\\\\t = \frac{471\ m}{80\ m/s}\\\\\)

t = 5.89 s

2.

Now, we analyze the vertical motion. Using 2nd equation of motion:

\(h = v_{i}t + \frac{1}{2}gt^2\)

where,

h = height of cliff = ?

vi = vertical component of initial speed of ball = 0 m/s(ball was shot horizontally)

g = acceleration due to gravity = 9.81 m/s²

t = time of flight = 5.89 s

Therefore,

\(h = (0\ m/s)(5.89\ s) + \frac{1}{2}(9.81\ m/s^2)(5.89\ s)^2\)

h = 170 m

3.

Now, we can use 1st equation of motion:

\(v_{f} = v_{i} + gt\\v_{f} = 0 m/s + (9.81\ m/s^2)(5.89\ s)\\\)

Vf = 57.8 m/s

The resultant of the displacement is 336.5m

The process of splitting a vector into its components is called resolution of the vector. The vectors are splitted into vertical and horizontal component.

For the first displacement;

The vertical component = - 150 sin45 = -106.1 m

The horizontal component = - 150 cos 45° = -106.1 m

For the second displacement;

The vertical displacement = - 85sin90 = -85

The horizontal component = 0

For the third displacement;

The vertical displacement = 550 sin55 = 450.5

The horizontal displacement = 550 cos 55 = 315.5

Sum of vertical component = 450.5-85-106.1 = 263.4

sum of horizontal component = 315.5 -106.1 = 209.4

Using Pythagorean theorem

R = √ 263.4² + 209.4²

R = √113227.92

R = 336.5m

The resultant angle = tan^-1( 263.4/209.4)

= tan^-1(1.26)

= 51.56°

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Answer:

2.1 rad/s

Explanation:

Given that,

Mass of a tether ball, m = 0.546 kg

Length of a rope, l =  4.56 m

The maximum tension the rope can withstand before breaking is 11.0 N

We need to find the maximum angular speed of the ball. Let v is the linear velocity. The maximum tension is balanced by the centripetal force acting on it. It can be given by :

\(F=\dfrac{mv^2}{r}\\\\v=\sqrt{\dfrac{Fr}{m}} \\\\v=\sqrt{\dfrac{11\times 4.56}{0.546}} \\\\=9.584\ m/s\)

Let \(\omega\) is the angular speed of the ball. The relation between the angular speed and angular velocity is given by :

\(v=r\omega\\\\\omega=\dfrac{v}{r}\\\\=\dfrac{9.584}{4.56}\\\\=2.1\ rad/s\)

So, the maximum angular speed of the ball is 2.1 rad/s.

Power is the RATE at which energy changes or flows.

The unit of energy is the Joule, so a unit of power is the Joule/second.

That unit has the special name "Watt".

Your question is not necessarily a question. It's also a statement, You could write

"Watt's the basic unit of the measurement of power".

Answer:

Watt

Explanation:

The metric unit of power is called a watt. One watt of power is equivalent to one joule of work being performed in one second. The joule is the unit of measurement of work or energy, and the Newton is the unit of measure for force.

PF

3.37 ev  is the maximum kinetic energy in eV of electrons ejected from sodium metal by 2.2 x 102-nm EM radiation

E=hc/ λ

E= \((6.63 *10^-34*3*10^8/220 *10^-9\)

E=5.65-2.28

E=3.37eV

A moving item or particle might have power of a certain sort called kinetic energy. When work, which entails the transfer of energy, is done on an object by applying a net force, that object acquires kinetic energy. Kinetic energy, which depends on an item or particle's mass and velocity of motion, is a property of motion. Any combination of vibration, axis rotation, translation (or movement along a route from one place to another), and translation are all examples of motion. The translational kinetic energy of a body is equal to 1/2mv2, which is calculated by multiplying the mass, m, by the square of the speed, v.

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The position of the body at time t is s (t) = -3 + 2t - 2 sin(2t³).

The position of the body at time t is calculated by applying the second kinematic equation as shown below.

s = s₀  + vt + ¹/₂at²

where;

The position at time t is calculated as;

s (t) = -3 + 2t + ¹/₂( - 4sin 2t )t²

s (t) = -3 + 2t - 2 sin(2t³)

Thus, the final position of the body is a function of the acceleration, initial velocity and time of motion of the body.

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sorry, it's B, not a made a mistake in the approximation

Answer:

tectonic plates are the outer portion of Earth's crust made up of huge pieces of rock.

The outer portion of the crust of the earth is made up of huge rocks, and they are known as tectonic plates.

The widely recognized scientific concept known as tectonic plates postulates that the Earth's earth's crust is made up of many sizable tectonic plates that have been steadily moving with around 3.4 billion years.

The theory of plate tectonics theory, which was established in the early to mid-twentieth century, is the foundation of the model. Following the confirmation of mid-ocean ridges in the mid or late 1960s, plate tectonics became widely accepted by geologists.

There are seven to eight primary plates and multiple lesser plates or "platelets" that make up the solid outer shells of the planet, known as the lithosphere, on Earth. The kind of tectonic plate, divergent, or transform—depends on the relative speed of the continents where they converge.

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The net force on q1 is 9.94 N.

From Coulomb's Law, the force between two point charges is given by:

where;

All the charges have the same charge and magnitude and are separated by the same distance.

The force between q1 and q2 is:

F12 = (9 * 10⁹ N * m²/C²) * (-2.35 x 10⁻⁶ C)² / (0.100 m)²

F12 = 4.97 N

The positive sign indicates that the force is repulsive

Similarly, the force between q2 and q3 is:

(9 * 10⁹ N * m²/C²) * (-2.35 x 10⁻⁶ C)² / (0.100 m)²

F12 = 4.97 N

The positive sign indicates that the force is repulsive

The net force on q1 will be:

Fnet = F12 + F23

Fnet = 4.97 N + (4.97)

Fnet = 9.94 N

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Answer:

salt

Explanation:

salt is a component for many acid base reactions

Answer:

  $900 trillion

Explanation:

If Alaska is 20% of the contiguous US, then the approximate area of interest is ...

  1200 miles × 3000 miles = 3.6×10^6 square miles.

The size of a dollar bill is about ...

  (6.5 cm)·(15.5 cm) = 100.75 cm^2

One mile is 160,934.4 cm, so 1 square mile is about ...

  1 mi^2 = (160,934.4 cm)^2 ≈ 2.59·10^10 cm^2

The number of dollars of interest is then ...

  (3.6 · 10^6 mi^2)(2.59 · 10^10 cm^2)/(100.75 cm^2) ≈ 9.3·10^14

  ≈ 930 × 10^12 . . . dollars

It would cost about 900 trillion dollars to cover the land area of the US in $1 bills.

The correct answers to the blanks are 1. UP ,2. UP and 3. ZERO

When the cart is initially given a push up the ramp, the direction of the acceleration of the cart is up the ramp. This is because the net force acting on the cart is directed up the ramp, in the same direction as the component of the gravitational force that is parallel to the ramp. As a result, the cart accelerates up the ramp in the same direction as the net force.

When the cart turns around and begins moving down the ramp, the direction of the acceleration of the cart is still up the ramp. This is because the component of the gravitational force that is parallel to the ramp is still directed down the ramp, but the net force acting on the cart is directed up the ramp due to the normal force exerted by the ramp on the cart. As a result, the cart accelerates down the ramp in the opposite direction to the net force, which is up the ramp.

            At the highest point that the cart reaches on the ramp, when the cart momentarily comes to rest, the magnitude of the acceleration of the cart is zero. This is because at this point, the cart is at the highest point on the ramp and has stopped moving. As a result, the velocity of the cart is zero, and therefore the acceleration of the cart is also zero.

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