A Test Rocket Is Fired Straight Up From Rest With A Net Acceleration Of 20. 0 M/s2. After 4. 00 Seconds (2024)

Answer:

A coil having 45 loops

Explanation:

The strength of an electromagnet is proportional to the number of loops. So, when we have more loops, we will get mor strength. It means that the coil that will produce a magnetic field with the maximum strenght is a coil having 45 loops because 45 is the greatest number in the list.

Given that spring constant, k = 100 N/m and displacement, x = - 5mm = - 0.005 m

The formula of restoring force according to Hooke's law,

[tex]F=-kx[/tex]

Substituting the values, we get

[tex]\begin{gathered} F=-100(-0.005) \\ =\text{ 0.5 N} \end{gathered}[/tex]

Thus, the force is 0.5 N

A plane travels north at 300 km/h while another plane travels towards south at 300 km/h and yes they are moving with the same speed.

What is speed?

Speed is the ratio of distance traveled by an object in total time taken.

So, speed = distance/time

In the question given, the planes are moving at 300 km/h in different directions. One of the planes travels 300 km towards north in 1 hour, while the other plain travels towards south covering the same distance in 1 hour Using the relation between distance, time and speed, we can see that both the planes are moving with the speed of 300 km/h.

Speed is a scalar quantity, that is completely described by its magnitude and have nothing to do with the direction of a moving object.

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I hope this helps you

Explanation

The equation of a line is in point slope form when it looks like: y−y1=m(x−x1) Here, x and y are variables.

so, the answer is

point slope form

I hope this helps you

Given data

The vector in the x-direction is Cx = -105 m

The vector in the y-direction is Cy = - 88.2 m

The expression for the direction of the vector is given as:

[tex]\theta=\tan ^{-1}(\frac{C_y}{C_x})[/tex]

Substitute the value in the above equation.

[tex]\begin{gathered} \theta=\tan ^{-1}(\frac{-88.2\text{m}}{-105\text{ m}}) \\ \theta=40^o \end{gathered}[/tex]

Thus, the direction of the vector is 40 degrees.

The wavelength of the light in nanometers is 6.85 nm.

We need to know about electromagnetic waves to solve this problem. Light is included in electromagnetic waves. Electromagnetic waves can propagate without media. The speed of electromagnetic in vacuum media is equal to the speed of light. Hence, the wavelength and frequency can be determined as

c = λ . f

where c is the speed of light (3 x 10⁸ m/s), λ is wavelength and f is frequency.

From the question above, we know that

f = 4.38 x 10¹⁶ Hz

By substituting the given parameter, we can calculate the wavelength of light

c = λ . f

λ = c / f

λ = 3 x 10⁸ / 4.38 x 10¹⁶

λ = 6.85 x 10¯⁹ m

λ = 6.85 nm

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Given,

The weight of the student, w=557 N

The height of the stairway, h=4.5 m

Time interval in which the student climbs the stairway, t=29 s

(a) The work done is given by the difference in the initial and final potential energy,

That is

[tex]W=wh[/tex]

On substituting the known values,

[tex]\begin{gathered} W=557\times4.5 \\ =2506.5\text{ J} \end{gathered}[/tex]

Thus the work done by the student in climbing the stairway is 2506.5 J

(b) The power is given by the time rate of work done.

That is

[tex]P=\frac{W}{t}[/tex]

On substituting the known values,

[tex]\begin{gathered} P=\frac{2506.5}{29} \\ =86.43\text{ W} \end{gathered}[/tex]

Thus the power output of the student is 86.43 W

Newton's law of cooling relates the temperature of an object with the time. This law is the following:

[tex]T=(T_0-T_r)e^{rt}+T_r[/tex]

Where:

[tex]\begin{gathered} T=\text{ temperature at time "t"} \\ T_0=\text{ initial temperature} \\ T_r=\text{ temperature of the surroundings} \\ r=\text{ rate of }cooling \\ t=\text{ time} \end{gathered}[/tex]

Since we are asked to determien time we need to solve for "t". To do that we will subtract the temperature of the surrounding from both sides:

[tex]T-T_r=(T_0-T_r)e^{-rt}[/tex]

Now, we divide by the factor multiplying "e":

[tex]\frac{T-T_r}{T_0-T_r}=e^{-rt}[/tex]

Now, we use natural logarithm on both sides:

[tex]\ln (\frac{T-T_r}{T_0-T_r})=\ln (e^{-rt})[/tex]

Now, we use the following property of logarithms on the right side:

[tex]\ln e^x=x[/tex]

This means that we can lower the exponent, like this:

[tex]\ln (\frac{T-T_r}{T_0-T_r})=-rt[/tex]

Now, we divide both sides by "-r":

[tex]-\frac{1}{r}\ln (\frac{T-T_r}{T_0-T_r})=t[/tex]

Now, we substitute the values:

[tex]-\frac{1}{0.067}\ln (\frac{100F-72F}{180F-72F})=t[/tex]

Solving the operations:

[tex]20.15\min =t[/tex]

Therefore, the time to wait is 20.15 minutes.

zero

Explanation

we know that when derivantind the position function respecto to time we got the function for velocity, so we can integrate the given function to obtain the function for velocity

hence

Step 1

a) integrate to find the function for distance travelede

[tex]\begin{gathered} v(t)=t^2-2t \\ integrate \\ \int(t^2-2t)\text{ dt} \\ \int(t^2-2t)\text{ dt=}\frac{t^{2+1}}{2+1}-\frac{2t^{1+1}}{2} \\ \int(t^2-2t)\text{ dt=}\frac{t^3}{3}-t^2 \end{gathered}[/tex]

so

[tex]\begin{gathered} d(t)=\frac{t^3}{3}-t^2+C \\ C=initial\text{ distance , so c=0} \end{gathered}[/tex]

Step 2

now,we have the functio for the distance,

a) evaluate for t=0

[tex]\begin{gathered} d(t)=\frac{t^3}{3}-t^2 \\ d(0)=\frac{t^{3}}{3}-t^2=\frac{0^3}{3}-0^2=0-0=0 \\ d(0)=0 \end{gathered}[/tex]

b) evaluate for t=3 minutes

[tex]\begin{gathered} d(t)=\frac{t^3}{3}-t^2 \\ d(3)=\frac{3^3}{3}-3^2=\frac{27}{3}-9=9-0 \\ d(3)=0 \end{gathered}[/tex]

now, find the total distance traveled by the particle from t = 0 to t = 3 minutes., subtract the positions

[tex]distance=\Delta d=0m-0m=0m[/tex]

so, the total displacement would be zero,but :

the particle actually travels ,it start in negative direction,and then it moves to positive direction, after 3 minutes the particle is in the same place

so, the answer is zero

The type of object were astronomers likely observing is A comet.

A comet is an icy, small solar system body that, when passing close to the solar, warms and begins to launch gases, a method that is referred to as outgassing. This produces a visible atmosphere or coma, and on occasion also a tail.

Comets are cosmic snowballs of frozen gases, rock, and dust that orbit the sun. while frozen, they are the size of a small metropolis. whilst a comet's orbit brings it near the sun, it heats up and spews dust and gases right into a large sparkling head large than maximum planets.

Because the Moon moved aside, the skies dimmed and ESA's close-to-Earth item Coordination Centre (NEOCC) took another appearance, simplest to discover the threat of effect was dramatically falling. It has seen that been confirmed that 2022 AE1 will now not affect Earth and has been removed from ESA's threat listing.

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Disclaimer:- your question is incomplete, please see below for the complete question.

A. A comet

B. An asteroid

C. A meteor

D. A nebula

Use the given formula to find the speed of the wave. Next, use the following relation between the speed v, the period T and the wavelength λ to find the period:

[tex]v=\frac{\lambda}{T}[/tex]

a) Replace g=9.81 m/s^2 and d=0.75 cm (convert cm to m first) into the given formula:

[tex]0.75\operatorname{cm}=0.75\times10^{-2}m[/tex]

[tex]\begin{gathered} v=\sqrt[]{gd} \\ =\sqrt[]{(9.81\frac{m}{s^2})(0.75\times10^{-2}m)} \\ =0.27\frac{m}{s} \end{gathered}[/tex]

b) Isolate T from the equation and substitute v=0.27 m/s, λ=2.6 cm.

[tex]2.6\operatorname{cm}=2.6\times10^{-2}m[/tex]

[tex]\begin{gathered} v=\frac{\lambda}{T} \\ \Rightarrow T=\frac{\lambda}{v} \\ =\frac{2.6\times10^{-2}m}{0.27\frac{m}{s}} \\ =0.096s \end{gathered}[/tex]

Therefore, the speed of a wave in water that is 0.75 cm deep is 0.27 m/s, and if the wave has a wavelength of 2.6cm, its period is equal to 0.096s.

[tex]\begin{gathered} v=0.27\frac{m}{s} \\ T=0.096s \end{gathered}[/tex]

Given data:

* The radius of curvature of the convex mirror is R = 6 cm.

* The distance of the object from the convex mirror is u = - 12 cm.

Required: The nature of the image formed.

Equations needed:

The mirror formula:

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

The magnification formula:

[tex]m=-\frac{v}{u}=\frac{h_i}{h_o}[/tex]

Solution:

The focal length of the convex mirror is,

[tex]\begin{gathered} f=\frac{R}{2} \\ f=\frac{6}{2} \\ f=3\text{ cm} \end{gathered}[/tex]

The distance of the image formed is,

[tex]\begin{gathered} \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \\ \frac{1}{v}+\frac{1}{(-12)}=\frac{1}{3} \\ \frac{1}{v}-\frac{1}{12}=\frac{1}{3} \\ \frac{1}{v}=\frac{1}{3}+\frac{1}{12} \end{gathered}[/tex]

By simplifying,

[tex]\begin{gathered} \frac{1}{v}=\frac{4+1}{12} \\ \frac{1}{v}=\frac{5}{12} \\ v=\frac{12}{5} \\ v=2.4\text{ cm} \end{gathered}[/tex]

The positive value of image distance indicated that the virtual image is formed.

By the magnification formula,

[tex]\begin{gathered} m=\frac{-(2.4)}{-12} \\ m=0.2 \end{gathered}[/tex]

The positive value of magnification indicates that the upright image is formed.

The value of the magnification is less than 1, thus, a small size (diminished) image is formed.

Final Answer:

Location - 2.4 cm behind the convex mirror

Orientation - Upright

Size - Small size (or diminished)

Type - Virtual

Hence, option B is the correct answer.

The index of refraction of a medium is given by:

[tex]\begin{gathered} n=\frac{c}{v} \\ \text{ where } \\ c\text{ is the speed of light in vacuum and } \\ v\text{ is the speed of light in the medium } \end{gathered}[/tex]

Plugging the value given we have:

[tex]\begin{gathered} n=\frac{3\times10^8}{1.74\times10^8} \\ n=1.724137961 \end{gathered}[/tex]

Therefore, the index of refraction is 1.724137931

To find:

The equation for the given FBD.

Explanation:

The net force acting on an object is given by the sum of all the forces acting on the object.

Thus the net force acting on the given object in the vertical direction is given by,

[tex]F_{net}=F-f\text{ }\to\text{ \lparen i\rparen}[/tex]

From Newton's second law, the net force acting on an object is given by,

[tex]F_{net}=ma\text{ }\to\text{ \lparen ii\rparen}[/tex]

Thus from equations (i) and (ii), the equation for the given FBD is given by,

[tex]F-f=ma[/tex]

Final answer:

Thus the correct answer is option C.

Electric shock is a severe electrical hazard that happens when a person comes into contact with an electrified circuit.

Electric shock, fire, and arc flash are the three most dangerous aspects of electricity. In particular, an electrical shock happens when a human comes into contact with both wires of an electrical circuit, one wire of an electrified circuit and the ground, or a metallic part that has become energized by contact with an electrical conductor.The severity and effects of an electrical shock are determined by some factors, including the course through the body, the quantity of current, the length of exposure, and the skin condition (whether it is wet or dry). Water is an excellent conductor of electricity, so it will allow electricity current to flow more easily in through wet skin.

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Given data:

* The initial velocity of the rock is 5 m/s.

* The time taken by the rock is 7 seconds.

* The acceleration of the rock is,

[tex]g=9.8ms^{-2}[/tex]

Solution:

By the kinematics equation,

The distance traveled by the rock in the vertical direction is,

[tex]y=y_o+v_ot+\frac{1}{2}gt^2[/tex]

where y_o is the initial distance of the rock, y is the final distance after the time t, v_o is the initial velocity, and t is the time taken to reach the final distance,

Substituting the known values,

[tex]\begin{gathered} y=0+5\times7+\frac{1}{2}\times9.8\times7^2 \\ y=35+240.1 \\ y=275.1\text{ m} \end{gathered}[/tex]

Thus, the distance traveled by the rock in 7 seconds is 275.1 meter.

Answer:

Electric Motor

Electricity

Explanation:

Motors are devices that use electricity and magnetism to create motion. Electric motors work in a reverse process by using motion and magnetism to generate electricity.

If there is a 1st quarter moon on July 9, The approximate date of the next new moon is 30 July.

It is July 31st because A full Moon appears every 29.5 days. This is the time it takes for the Moon to go through one whole lunar phase cycle.

During the relaxation of the month, we see elements of the daylight aspect of the Moon, or phases. these eight levels are, in order, new Moon, waxing crescent, first area, waxing gibbous, complete Moon, waning gibbous, 1/3 area, and waning crescent. The lunar phase cycle repeats as soon as a month (every 29. five days).

The Moon presents these eight stages one after the alternative because it acts via its cycle every month. It takes 27 days for the Moon to orbit Earth. that means the Moon's cycle is 27 days long..

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In order to be a vector quantity, the quantity needs to have a direction, besides its magnitude.

For example, temperature has no direction, only magnitude, but velocity has direction and magnitude.

From these options, the only one that is a vector quantity is displacement, therefore the correct option is A.

302.038 °K

Explanation

to conver from Fahrenheit to kelvin, we can use this formula.

[tex]\mleft(F-32\mright)\times\frac{5}{9}+273.15=k[/tex]

then

Let

[tex]\begin{gathered} F=84 \\ \end{gathered}[/tex]

now, replace.

[tex]\begin{gathered} (F-32)\times\frac{5}{9}+273.15=k \\ \text{ }(84-32)\times\frac{5}{9}+273.15=k \\ \text{ }(52)\times\frac{5}{9}+273.15=k \\ 302.038=K \end{gathered}[/tex]

therefore, the answer is 302.038 °K

I hope this helps you

We will have that the flux density will be:

[tex]^{}\rho=\frac{0.6Wb}{120cm^2}\Rightarrow\rho=5\cdot10^{-3}Wb/cm^2[/tex]

The gravitational force of the shell exerts is 4.25m x 10¯¹² N.

We need to know about gravitational force to solve this problem. The gravitational force is the force caused by two masses of objects. The magnitude of gravitational force can be determined as

F = G.m1.m2 / R²

where F is the gravitational force, G is the gravitational constant (6.674 × 10¯¹¹ Nm²/kg²), m1 and m2 are the mass of the object and R is the radius.

From the question above, we know that

m1 = 1.6 kg

m2 = m

R = 5.01 m

By substituting the following parameters, we get

F = G.m1.m2 / R²

F = 6.674 × 10¯¹¹ . 1.6 . m / 5.01²

F = 4.25m x 10¯¹² N

where m is the mass of the shell

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Answer:

0.8 meters

Explanation:

When an object is moving at a constant velocity in a circular motion, the only acceleration acting on it is the centripetal acceleration which is directd toward the center of the circle

The formula for centripetal acceleration is

[tex]a_c = \dfrac{v^2}{r} \dots[1][/tex]

where
[tex]\text {$a_c$ is the centripetal acceleration}\\\\\text {$v$ is the velocity}\\\\\text{$r$ is the radius of the circular path}\\\\[/tex]

Given
[tex]a_c = 12\;m/s^2\\v = 3.1\;m/s[/tex]

we can plug in these values into the formula to determine r

[tex]12 = \dfrac{3.1^2}{r}[/tex]

[tex]r = \dfrac{3.1^2}{12} = \dfrac{9.61}{12} = 0.80 \;m[/tex]

Though there are at least a million asteroids, spacecraft like galileo survive their trip through the asteroid belt because they are widely spaced and spread out over large distances.

What is an asteroid belt?

In our solar system, the asteroid belt is found between the orbits of Mars and Jupiter containing millions of small-sized asteroid rocks.

In this asteroid belt, many rigid, irregularly shaped rock bodies are present which vary in their size.

However, for a spacecraft or a space probe, there is no chance of hitting any of the asteroids while on its way because these are widely spaced and are present at a large distance from one another.

In general, our space so big, wide, and empty that the chances of collision with an object are zero

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First, let's calculate the rocket velocity when it stops accelerating, using Torricelli's equation:

[tex]\begin{gathered} V^2=V^2_0+2\cdot a\cdot d \\ V^2=25.6^2+2\cdot2.34\cdot231 \\ V^2=655.36+1081.08 \\ V^2=1736.44 \\ V=41.67\text{ m/s}^2 \end{gathered}[/tex]

After the engine stops, the total acceleration will be the gravity acceleration, with a downwards direction and magnitude of 9.81 m/s².

The maximum height occurs when the velocity is zero, so we can use the formula below:

[tex]\begin{gathered} V=V_0+a\cdot t \\ 0=41.67-9.81\cdot t \\ 9.81t=41.67 \\ t=\frac{41.67}{9.81} \\ t=4.25\text{ s} \end{gathered}[/tex]

Now we need to calculate the time spent accelerating (engine turned on):

[tex]\begin{gathered} V=V_0+a\cdot t \\ 41.67=25.6+2.34\cdot t \\ 2.34t=41.67-25.6 \\ 2.34t=16.07 \\ t=\frac{16.07}{2.34} \\ t=6.87\text{ s} \end{gathered}[/tex]

Therefore the total time, since lift-off until maximum height, is:

[tex]\begin{gathered} t=6.87+4.25 \\ t=11.12\text{ s} \end{gathered}[/tex]

The rocket reaches the maximum height 11.12 seconds after lift-off.

Consider that only stars with masses in between 30 and 70 Sun's masses could be black holes. This is because only stars with enough mass have the enough gravitational force to overcome the radiation pressure of the star and thus cause the star to collapse and become a black hole.

UY Scuti has in between 7 and 10 Sun's masses, then, it is not possible this star becomes a black hole.

In case if UY Scuti has a mass above a certain threshold, it could potentially collapse into a black hole after the supernova event.

UY Scuti, the largest known star in terms of radius, is yet unknown as to its future development and destiny.

It is predicted that UY Scuti, a red supergiant star, will experience a supernova explosion at some point in the future.

A large star that goes supernova unleashes a tremendous amount of energy and experiences a catastrophic explosion.

Thus, the star's mass determines the explosion's specific consequence. After the supernova event, UY Scuti might possibly collapse into a black hole if its mass is greater than a predetermined limit.

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Given data

*The given mass of the person is m = 40 kg

*The value of the acceleration due to the gravity is g = 9.8 m/s^2

(A)

The reading on the scale is calculated when the elevator is stationary is given as

[tex]\begin{gathered} R=mg \\ =(40)(9.8) \\ =392\text{ N} \end{gathered}[/tex]

(B)

The formula for the reading on the scale when the elevator is moving up at constant speed is given as

[tex]\begin{gathered} N=mg \\ =(40)(9.8) \\ =392\text{ N} \end{gathered}[/tex]

(C)

The formula for the reading on the scale when the elevator accelerates upwards at 5.00 m/s^2 is given as

[tex]N=m(g+a)_{}[/tex]

Substitute the known values in the above expression as

[tex]\begin{gathered} N=(40)(9.8+5) \\ =592\text{ N} \end{gathered}[/tex]

(D)

The formula for the reading on the scale when the elevator accelerates downwards at 5.00 m/s^2 is given as

[tex]N=m(g-a)_{}[/tex]

Substitute the known values in the above expression as

[tex]\begin{gathered} N=(40)(9.8-5.0) \\ =192\text{ N} \end{gathered}[/tex]

All stars die in about 5 billion years — our sun will, too. The Sun will first become a Red Giant and then a white dwarf.

So the final stage is White dwarf.

Given:

The uses of LASER light

To find:

Which is not an application of LASER light

Explanation:

When cutting stainless steel or aluminium, LASER beams are used.

To remove warts, moles, sunspots, and tattoos in human bodies LASER lights are used.

LASER is used in communication also. Laser communication in space is the use of free-space optical communication in outer space.

One of the most important uses for lasers in astronomy is to reduce distortion on images taken with ground-based telescopes. So directly we cannot say that LASER is used for the calibration of telescopes.

Hence, calibration of telescopes is not an application of LASER light.

c) To determine the velocity of the motion at the given time, consider that the velocity is also the area under the line of the graph a vs t.

Between t=0s and t = 2 s, the area under the line is:

A1 = 2 X 2 = 4

Then, until t = 2s the velocity is 4 m/s

The area between t = 2s and t = 4 s is:

A2 = 2 x 0 = 0

The area between t = 4s and t = 5s, the area is:

A3 = 2 x 1 = 2

Now, consider that the velocity is the sum of the previous areas, but taking areas on the negative y-axis as negative ones. Then, you have:

A = A1 + A2 - A3 = 4 + 0 - 2 = 2

Hence, the velocity is 2 m/s