Q1.A toy rocket is launched with an initial velocity of 11.0 m/s in the horizontal direction from the roof of a 40.0 m -tall building. The rocket's engine produces a horizontal acceleration of (1.60 m/s3)t, in the same direction as the initial velocity, but in the vertical direction the acceleration is g , downward. Air resistance can be neglected.
Part A) What horizontal distance does the rocket travel before reaching the ground? write the answer with the unit.

The gazelle escapes the cheetah by 7.5 meters. This is calculated by determining the distance the cheetah and gazelle each cover in the given time. The gazelle's distance includes both the acceleration phase and the constant speed phase.

To determine if the gazelle escapes from the cheetah, we need to calculate the distance both the gazelle and the cheetah cover separately within the same time frame. The cheetah can maintain its top speed of 30 m/s for only 15 seconds. Therefore, the total distance covered by the cheetah while it's at top speed is given by:

Distance covered by the cheetah = speed × time = 30 m/s × 15 s = 450 m

The gazelle starts accelerating at 4.6 m/s2 for 5.0 seconds. The distance covered by the gazelle during acceleration can be calculated using the equation:

Distance = 0.5 × acceleration × time2 = 0.5 × 4.6 m/s2 × (5.0 s)2 = 57.5 m

After 5 seconds of acceleration, the gazelle will be running at a constant speed, which we can find using the formula:

Final velocity = initial velocity + (acceleration × time) = 0 + (4.6 m/s2 × 5.0 s) = 23 m/s

For the remaining 10 seconds (since the cheetah runs at top speed for 15 seconds and the gazelle has already spent 5 seconds accelerating), the gazelle travels at this constant speed, covering:

Distance at constant speed = speed × time = 23 m/s × 10 s = 230 m

The total distance covered by the gazelle is the sum of the distance covered during acceleration and the distance covered at constant speed:

Total distance covered by gazelle = 57.5 m + 230 m = 287.5 m

Now we need to add the initial distance between the gazelle and the cheetah to the distance covered by the gazelle, to find out how far the gazelle is when the cheetah stops:

Total distance from cheetah = initial distance + distance covered by gazelle = 170 m + 287.5 m = 457.5 m

Since the cheetah covers only 450 m and the gazelle is 457.5 m away from the cheetah's starting point, the gazelle escapes, and the distance by which it's in front when the cheetah gives up is:

Escape distance = total distance from cheetah - distance covered by cheetah = 457.5 m - 450 m = 7.5 m

Therefore, the gazelle escapes the cheetah by 7.5 meters.

Final answer:

Efficiency comparison between theoretical and actual values in power plants due to various factors.

Explanation:

The maximum theoretical efficiency of a heat engine operating between 300°C and 27°C can be calculated using the Carnot efficiency formula.

The ideal efficiency in this case would be 67%.

The actual efficiency of nuclear power plants is lower than the ideal efficiency due to losses in energy conversion, limitations of materials, and safety considerations.

Efficiency in real-world applications is affected by factors like temperature limitations, friction losses, and energy transfer inefficiencies.

The wavelength of a microwave is longer than that of visible light, with microwaves typically ranging from 1 millimeter to 1 meter while visible light ranges between ~400 and 700 nanometers. In terms of scale, these differ by about 6-8 orders of magnitude.

The wavelength of a microwave is indeed longer than that of visible light. To understand this, it helps to remember that the type of wave - whether it's a microwave, visible light, ultraviolet light, etc. - is determined by its frequency or wavelength in the electromagnetic spectrum. Microwaves, used largely in radar and communications, possess longer wavelengths ranging from 1 millimeter to 1 meter. Visible light, on the other hand, has shorter wavelengths, between approximately 400 and 700 nanometers.

In terms of the orders of magnitude difference, we can observe a substantial difference. The difference in wavelength between visible light and microwaves is generally in the range of 6-8 orders of magnitude, taking the range of both wavelengths into account. This significant disparity illustrates the vast variety and scale within the electromagnetic spectrum.

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Solenoid

A coil of wire that carries an electric current is a solenoid

Final answer:

The amount of thermal energy created by friction during Justin's descent is 0.537 J.

Explanation:

To calculate the thermal energy created by friction during Justin's descent, we need to find the change in mechanical energy. The mechanical energy at the top consists of gravitational potential energy and kinetic energy. At the bottom, it consists of only kinetic energy. Since there is no change in the height, the change in mechanical energy is equal to the work done by friction, which can be calculated using the equation:

Work = Change in mechanical energy = Kinetic energy at the bottom - Gravitational potential energy at the top

First, we need to calculate the gravitational potential energy at the top:

Gravitational potential energy (PE) = mass * gravity * height

Substituting the given values:

PE = 0.03 kg * 9.8 m/s² * 8.0 m = 2.352 J

Next, we need to calculate the kinetic energy at the bottom:

Kinetic energy (KE) = 0.5 * mass * velocity²

Substituting the given values:

KE = 0.5 * 0.03 kg * (11 m/s)² = 1.815 J

Now we can calculate the work done by friction:

Work = KE - PE = 1.815 J - 2.352 J = -0.537 J

Since work is a scalar quantity with no direction, the negative sign indicates that the work is done by friction rather than by the object. Therefore, the amount of thermal energy created by friction during Justin's descent is 0.537 J.

Answer:

T= 1 / 8.93 . 10^7

Explanation:

If an object is traveling east and slowing down, its acceleration is westward or negative when east is considered positive. This negative acceleration is indicative of deceleration.

If an object is traveling east with a decreasing speed, the direction of the object's acceleration is to the west. Acceleration is defined as the rate of change of velocity. If an object is slowing down, its acceleration is in the opposite direction of its velocity. When we consider east as the positive direction, and the object is moving east but slowing down, it means the object has a negative acceleration because it is accelerating toward the west. This is often referred to as deceleration. A real-world example could be an airplane landing on an eastward facing runway; as it comes to a stop, it experiences negative acceleration.

The passage explains the Copernican Principle and its implications on our understanding of our place in the universe.

The passage you provided can be best described as an explanation of the Copernican Principle and its implications on our understanding of our place in the universe. The Copernican Principle, named after Nicolaus Copernicus, states that Earth is not the center of the solar system, and this idea has expanded to understand that our solar system is not the center of our galaxy and our galaxy is not the center of the universe. This perspective reminds us that we should not view ourselves as the center of everything.

Final answer:

To find the heights at which the wire should be attached to each pole, we can use the concept of similar triangles. By setting up an equation involving the height of one pole and the height difference between the poles, we can solve for the heights. The wire should be attached to the first pole at a height of approximately 39.64 ft and to the second pole at a height of approximately 0.36 ft.

Explanation:

To determine the heights at which the wire should be attached to each pole, we can use the concept of similar triangles. Let's call the height at which the wire is attached to the first pole h1, and the height at which it is attached to the second pole h2.

Since the lowest point of the wire is 19 ft above the ground, and the poles are 40 ft apart, we can use the Pythagorean theorem to find the length of the vertical leg of the right triangle formed by the wire and the ground. This will be the difference between the heights of the two poles:

|h1 - h2| = sqrt(41^2 - 19^2)

We know that the wire is 40 ft above the ground at its highest point. So if we subtract the height at which it is attached to one pole from 40 ft, we can find the height at which it is attached to the other pole:

h2 = 40 - h1

By substituting this expression for h2 into the equation |h1 - h2| = sqrt(41^2 - 19^2), we can solve for h1:

|h1 - (40 - h1)| = sqrt(41^2 - 19^2)

Simplifying further, we get:

2h1 - 40 = sqrt(41^2 - 19^2)

Adding 40 to both sides of the equation:

2h1 = 40 + sqrt(41^2 - 19^2)

Finally, dividing both sides by 2, we find:

h1 = (40 + sqrt(41^2 - 19^2))/2

By plugging in the values and performing the calculations, we find that h1 ≈ 39.64 ft and h2 ≈ 0.36 ft.

The car will catch up to the truck in approximately 0.459 minutes, or about 27.54 seconds, by traveling at a relative speed of 17 km/h faster than the truck.

To determine how long it will take for the car traveling at 92 km/h to reach the truck traveling at 75 km/h, we need to calculate the relative speed between the two vehicles and then use that information to find out how long it takes to cover the distance between them.

Step 1: Calculate Relative Speed

The car's speed is 92 km/h and the truck's speed is 75 km/h. To find the relative speed, we subtract the slower speed (truck) from the faster speed (car):

92 km/h - 75 km/h = 17 km/h

Step 2: Calculate Time to Cover the Distance

Now that we have the relative speed, we can calculate the time it will take for the car to cover the 130 meters (0.130 kilometers) separating it from the truck.

Time = Distance / Speed

Time = 0.130 km / 17 km/h

Time = 0.00765 hours

Converting 0.00765 hours into minutes (as there are 60 minutes in an hour) gives us:

Time = 0.00765 hours x 60 minutes/hour = 0.459 minutes

Thus, it will take approximately 0.459 minutes, or about 27.54 seconds, for the car to reach the truck.

According to Dr. Spock's child-rearing philosophies, parents ought to respect and foster children's individuality and decision-making skills. Therefore, he would likely endorse parental actions such as allowing the 2-year-old to pick her clothes, letting the infant explore her surroundings, and supporting the 18-year-old's life choices.

Dr. Spock, well-known pediatrician and author, strongly believed in the importance of recognizing a child's individuality and fostering independence. Hence, he would likely endorse the parents' actions in C. Your two-year-old daughter refuses to wear the clothes you pick for her every morning, which makes getting dressed a twenty-minute battle. Spock would perceive this as the child developing personal decision-making skills. He would also support A. Your infant daughter puts everything in her mouth, including the dog's food.

For him, exploring the environment plays a crucial role in a child's early development. However, he would suggest that parents keep a close eye on their child to ensure safety. Finally, he might approve of E. Your 18-year-old daughter has decided not to go to college. Instead she's moving to Colorado to become a ski instructor, recognizing it as the young adult exercising her rights to make life choices.

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After leaving the plane, the block will have an unknown speed (S),

which can be broken into x,y components.

 The x,y kinematics are: x – 1

x0 - 0 V - ? V0 - Scos(-30)

a – 0

t - t

y - 0

y0 – 1

V - ?

V0 - Ssin(-30)

a - -9.8

t – t

We then use x=x0+v0t+.5at^2

in the x case: 1=0+Scos(-30)+.5(0)t^2

Solving for t gives t=1/ Scos(-30)

in the y case,

with t-substitution:

0=1+Ssin(-30)*1/Scos(-30)+.5(-9.8)(1/Scos(-30))^-2

In the middle velocity term, S cancels out. Multiplying all known numbers as well as squaring the third term gives:

 0=1-.5774-6.5333/S^2

Solving for S = S = 3.9319 m/s

Now with a mark on final ramp speed, we can now make a 3rd kinematics equation. The acceleration will be altered from gravity:

Slide force = 9.8*sin(30) = 4.9 m/s^2.

x - ?

x0 – 0

V - 3.9319

V0 – 0

a - 4.9

t - ?

So the equation we use is V2 = V02+2a(x-x0). 3.93192=0+2*4.9*(x-0)

Solving for x gives x=1.5775 m up the ramp.

So we now look for the y component of the ramp length:

1.5775*sin(30) = .78875 m 'high' on the ramp. 

Final answer:

The block should be released from a height of h = 1.732m (rounded to three decimal places) in order to land in the hole.

Explanation:

The block will land in the hole if it is released from a certain height h on the ramp. To find this height, we can break down the problem into two parts:

So, the block should be released from a height of h = 1.0m/tan(30) = 1.732m (rounded to three decimal places) in order to land in the hole.

The heat transfer, in kJ per kg of water, is 2510.4 kJ.

The heat transfer, in kJ per kg of water, can be calculated using the formula:

Heat transfer = specific heat capacity × mass of water × change in temperature

Given that the specific heat capacity of water is 4.184 J/g °C and the mass of water is 1 kg, the heat transfer can be calculated as:

Heat transfer = (4.184 J/g °C) × (1000 g) × (400 - 100) °C = 2510400 J = 2510.4 kJ

Therefore, the heat transfer is 2510.4 kJ per kg of water.

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Final answer:

The speed of the mass at the instant when the kinetic and potential energies are equal is v = vmax / √2, which is 0.707 times the maximum speed vmax.

Explanation:

When dealing with an oscillating mass on a spring, the maximum kinetic energy occurs when the potential energy is at a minimum, which is at the equilibrium position. Conversely, the potential energy reaches its maximum value when the kinetic energy is zero, which occurs at the maximum displacement from equilibrium. According to the conservation of mechanical energy, the total energy in the system is constant and is shared between the kinetic and potential energies.

The condition where the kinetic energy (K) and potential energy (U) are equal can be represented by the equation K = U. Since the total energy is the sum of the kinetic and potential energies, we can derive an expression where E = K + U, and at the point where K = U, they each are equal to E/2, where E is the total energy of the system. Thus, K = 1/2 mv2 = E/2. We know that the maximum kinetic energy (when the potential energy is zero) is given by Kmax = 1/2 mvmax2, which is equal to the total energy E.

To find the speed v when kinetic and potential energies are equal, we set the kinetic energy expression to E/2 and solve for v:

1/2 mv2 = 1/2 mvmax2 / 2

v2 = vmax2 / 2

v = vmax / √2

Therefore, the speed of the mass when the kinetic and potential energies are equal is vmax / √2, which is 0.707 times the maximum speed vmax.

Answer:

Acceleration after throwing is 0.2m/s²

Acceleration before throwing is 0 m/s² since the force is zero

Explanation:

By Newtons third law we have force applied by ball on person = 10 N

Mass of person plus skateboard = 50 kg

We also know the equation

     Force, F = mass x acceleration

                 F = ma

    Here F = 10 N

             m = 50 kg

Substituting,

              10 = 50 x a

                 [tex]a=\frac{10}{50}=\frac{1}{5}=0.2m/s^2[/tex]

Acceleration after throwing is 0.2m/s²

Acceleration before throwing is 0 m/s² since the force is zero

To calculate the kilocalories generated when the brakes are used to bring a car to rest, determine the initial kinetic energy of the car using the formula KE = 0.5 * mass * velocity^2, and then convert it into kilocalories using the conversion factor 1 kcal = 4186 J.

To calculate the kilocalories generated when the brakes are used to bring a car to rest, we need to determine the initial kinetic energy of the car and then convert it into kilocalories using the conversion factor provided.

The initial kinetic energy of the car can be calculated using the formula: KE = 0.5 * mass * velocity^2. Plugging in the given values, KE = 0.5 * 1200 kg * (95 km/h)^2 = 0.5 * 1200 kg * (95^2) km^2/h^2.

Now, to convert the kinetic energy from joules to kilocalories, we can use the conversion factor: 1 kcal = 4186 J. Thus, the kilocalories generated when the brakes are used to bring the car to rest would be the kinetic energy in joules divided by 4186 J/kcal.

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Answer:

Δx=vₓΔt

Explanation:

edge 2020 answer (D)

The ball is in the air for about 5.5 seconds when it is thrown vertically up.

Acceleration is rate of change of velocity.

[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]

[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem!

This problem is about Projectile Motion

Given:

initial speed = u = 27 m/s

Unknown:

time interval of the ball in the air = t = ?

Solution:

[tex]h = u \sin \theta ~t - \frac{1}{2}gt^2[/tex]

[tex]0 =  u \sin \theta ~t - \frac{1}{2}gt^2[/tex]

[tex]u \sin \theta ~ t = \frac{1}{2}gt^2[/tex]

[tex]u \sin \theta = \frac{1}{2}gt[/tex]

[tex]t = \boxed {\frac{ 2u \sin \theta }{g}}[/tex]

If the angle of projection = θ = 90° , then :

[tex]t = \boxed {\frac{ 2(27) \sin 90^o }{9.8}}[/tex]

[tex]t \approx 5.5 ~ seconds[/tex]

If the angle of projection = θ = 45° , then :

[tex]t = \boxed {\frac{ 2(27) \sin 45^o }{9.8}}[/tex]

[tex]t \approx 3.9 ~ seconds[/tex]

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle

Answer:

the answer is natural gass

Explanation:

Answer:

O is an element, And H2O2 is an compound

Explanation:

Answer:

the other person is correct

Explanation:

The north and south forces first cancel each other out, leaving a net force of 20 N towards the south. Adding this to the westward force of 40 N using the Pythagorean theorem results in a net force of 44.7 N.

The forces acting on the object in this problem are 20 N north, 40 N south, and 40 N west. When combining these forces, we consider that the forces act in different directions, and so the north-south forces will cancel each other out to some extent. The net north-south force is 40 N south minus 20 N north, resulting in a 20 N force towards south. The westward force is 40 N, and the net force of the object can be calculated using the Pythagorean Theorem:

Net Force = √ [ (20 N)² + (40 N)² ] = √ [ 400 + 1600] = √ [ 2000 ] = 44.7 N

Thus, the magnitude of the net force on the object is 44.7 N.

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