It was a dark and stormy night, when suddenly you saw a flash of lightning. Three-and-a-half seconds later you heard the thunder. Given that the speed of sound in air is about 340 m/s, how far away was the lightning bolt?

Density of given salt solution is 1.14 gram / milliliter

Given:

Mass of salt solution = 57 gram

Volume of salt solution = 50 milliliter

Find:

Density of a salt solution

Computation:

⇒ Density = Mass / Volume

⇒ Density of a salt solution = Mass of salt solution / Volume of salt solution

⇒ Density of a salt solution = 57 / 50

⇒ Density of a salt solution = 1.14 gram / milliliter

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Answer:

30 hours

Explanation:

Total distance from the coast to the storm = 450+150 = 600 Nmi

Speed of the hurricane = 20 knots = 20 Nmi/h

Time taken by the hurricane to reach the coast

[tex]\text{Time}=\frac{\text{distance}}{\text{Speed}}\\\Rightarrow \text{Time}=\frac{600}{20}=30 \\\Rightarrow \text{Time}=30 hours[/tex]

∴ Tropical storm-force winds begin to affect the community by 30 hours

Time taken by the eye to reach the coast

\text{Time}=\frac{450}{30}=15 hours[/tex]

Why does a gun recoil when a bullet is fired?

When a bullet is fired, the gun exerts a force on the bullet through the trigger (this is action) in a particular direction. According to Newton's Third Law, we know to every action there is an equal and opposite reaction; action and reaction act on different bodies. So, the bullet will also exert an equal and opposite reaction on the gun in the opposite direction. That is why a gun recoils when a bullet is fired from it.

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The acceleration of an airplane will be "4 m/s²".

According to the question,

The velocity is:

The time is:

As we know,

The formula of acceleration is:

→ [tex]A = \frac{Change \ in \ velocity}{Time}[/tex]

or,

→ [tex]A = \frac{v_2-v_1}{t}[/tex]

By substituting the values, we get

→     [tex]= \frac{80-0}{20}[/tex]

→     [tex]=\frac{80}{20}[/tex]

→     [tex]= 4 \ m/s^2[/tex]

So the above answer is right.

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Answer:

Mass = 30.6 kg

Explanation:

Given

Weight scale reading W = 300 N

Solution

Weight W = Mass (m) x Acceleration due to gravity (g)

W = mg

m = W/g

m = 300 / 9.81

m = 30.6 Kg

A bathroom scale measures weight which is a force in newtons or pounds. It is calibrated to provide information about mass by dividing the weight measurement by 9.80 in most countries. In this case, if each scale reads 300 N, Larry's mass would be approximately 30.61 kg.

A bathroom scale measures weight, which is a force in newtons or pounds. When you stand on a bathroom scale, the springs inside the scale compress in proportion to your weight, similar to rubber bands expanding when pulled. This compression provides a measure of your weight.

However, the scale is calibrated to provide information about mass, so the weight measurement is divided by 9.80 in most countries to give a reading in mass units of kilograms.

In this case, if each scale reads 300 N, we can use the formula F = mg, where F is the force (300 N), m is the mass (unknown), and g is the acceleration due to gravity (approximately 9.80 m/s²). Rearranging the formula, we have m = F/g. Substituting the given values, we get m = 300 N / 9.80 m/s² = 30.61 kg.

The centripetal acceleration (a ) of an object moving in a circular path of radius  r at a constant speed and v is  = a = v²/r

The riders are subjected to a centripetal acceleration that is 1.50 times the acceleration due to gravity, a = 1.50 × g.

a = r  ×ω ²  

1.50 g = r  ×ω ²  

ω ²   = √1.50 g / r

rpm =  ω/2π  ×60

rpm=  √1.50⋅g/ r/2 π  ×60

rpm = 9.50

Therefore,  the riders will be subjected to approximately 9.50 revolutions per minute.

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Answer:

Explanation:

Scalar quantity is described as such quantities measured which has only magnitude but not direction.

Force when applied on any object is always denoted and comes with direction. It is always necessary to represent force is acting on which direction.

Hence force is not a scalar quantity. It is a vector quantity as it has magnitude as well as direction.

Having and drinking hygienic water is human right and is vital to life. The water should be tested, treated and filtered to remove any contaminants that can lead do sickness. Some of the strategies in which local municipality is implementing in addressing the topic of lack of clean water are:
1. Good monitoring of the water supplies
2. Desalination – this is removal of mineral components from saline water especially salt. The procedure is more expensive but is a way to reuse water 
3. Campaign for more proficient and more wisely usage of the water in order to make the people conscious of the fact how important the natural resource water is.

The total force to slide the bank safe is 795 N. The normal force exerted by the safe on the floor is 2943 N. Hence, the coefficient of kinetic friction on the bank floor is 0.27.

To find the coefficient of kinetic friction, we first need to determine the total force used to move the safe. Bonnie and Clyde are both applying their forces to move the safe in the same direction. So, we add Clyde’s force to Bonnie's force. This gives us a total force of 795 N (445 N + 350 N).

Since the safe slides at a constant speed, it means the applied force is equal to the friction force. Therefore, the friction force is also 795 N. We calculate the normal force which is the weight of the safe, that is mass times the gravity. The mass of the safe is 300 kg and the gravity is approximately 9.81 m/s². Therefore, the normal force is 2943 N (300 kg×9.81 m/s²).

Now, we use the formula of kinetic friction, which is the friction force divided by the normal force, to find the coefficient of kinetic friction. Therefore, the coefficient of kinetic friction on the bank floor is 0.27 (795 N / 2943 N).

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we know that

[tex] 1 [/tex] nanometer is equal to [tex] 10^{-9} [/tex] meters

so

[tex] 650\ nm [/tex]------> convert to meters

by proportion

[tex] \frac{1}{10^{-9}}\frac{nm}{m} = \frac{650}{x} \frac{nm}{m} \\ \\ x=650*10^{-9} \ nm\\ \\ x=6.5*10^{-7} \ m [/tex]

[tex] Wave\ length\ of\ red\ light = 6.5*10^{-7}\ m [/tex]

[tex] Wave\ length\ of\ a\ water = 2\ m [/tex]

To calculate how much bigger is the wavelength of a water

Divide [tex] 2\ m [/tex] by [tex] 6.5*10^{-7}\ m [/tex]

so

[tex] \frac{2}{6.5*10^{-7}} =3.08*10^{6} [/tex]

therefore

the answer is

[tex] 3.08*10^{6}\ times\ bigger [/tex]

The wavelength of the water wave is 3 x 10⁶ times bigger than that of the red light.

The wavelength of a waveform signal that is propagating in space or over a wire is measured by the separation between identical points, adjacent crests in the adjacent cycles.

Given that the wavelength of red light is 650 nanometers.

We know that 1 nanometer = 10⁻⁹meter

In order to convert 1 nanometer into meter, it should be multiplied by 10⁻⁹.

So, 650 nm = 650 x 10⁻⁹

650 nm = 0.65 x 10⁻⁶

The wavelength of the given water wave = 2 m

So, comparing the wavelength of the red light with that of the water wave,

2/ 0.65 x 10⁻⁶ = 3 x 10⁶

Therefore, the wavelength of the water wave is 3 x 10⁶ times bigger than that of the red light.

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Answer:

D.55.86 N

Explanation:

Final answer:

The radius of curvature for a car rounding a curve with a constant speed of 10 m/s and a centripetal acceleration of 5 m/s2 is calculated to be 20 meters.

Explanation:

The problem requires us to find the radius of curvature when a car is rounding a curve with a centripetal acceleration. Centripetal acceleration (a) is given by the formula a = v² / r, where v is the constant speed of the car and r is the radius of curvature. Knowing that the car has a constant speed (10 m/s) and a centripetal acceleration (5 m/s²), we can rearrange this formula to solve for the radius r as follows:

r = v² / a

Substituting the given values:

r = (10 m/s)² / (5 m/s²)

r = 100 m²/s² / 5 m/s²

r = 20 m

Therefore, the radius of curvature of the curve is 20 meters.

No, because a single distance could

correspond to a variety of different positions of the objects.

Final answer:

An astronaut could theoretically throw a wrench approximately 73.5 meters high on the Moon, which is about 6 times higher than on Earth, due to the lower gravitational acceleration.

Explanation:

The question is about how high an astronaut could throw a wrench on the Moon compared to the Earth given the same starting speed. The gravitational acceleration on the Moon is 0.170 g, or approximately 1.6 m/s², which is about 1/6 of that on Earth (9.8 m/s²). Therefore, if an astronaut can throw a wrench 12.0 meters high on Earth, we can calculate how high it would go on the Moon using the ratios of the accelerations due to gravity.

First, we recognize that the maximum height reached by an object thrown vertically is inversely proportional to the local gravitational acceleration. Mathematically:

Height on Earth / Height on Moon = Acceleration due to gravity on Moon / Acceleration due to gravity on Earth

Substituting the given values:

12.0 m / Height on Moon = 1.6 m/s² / 9.8 m/s²

Solving for the height on the Moon gives:

Height on Moon = 12.0 m * (9.8 m/s² / 1.6 m/s²) = 12.0 m * 6.125 = 73.5 m

Therefore, the astronaut could throw the wrench approximately 73.5 meters high on the Moon, assuming no air resistance and the same initial throwing speed.

The recoil velocity of the machine is 0.11 m/s in opposite direction.

According to the law of conservation of momentum, when two or more bodies are operating upon one another in an isolated system, their combined momentum stays constant unless an external force is added. Because of this, momentum cannot be created or destroyed.

The mass of the pitching machine is : M = 54.6 kg

The mass of the baseball is: m = 0.149 kg.

The velocity of the baseball is: v = 42.6 m/s.

The velocity of the machine is: V = ?

From law of conservation of momentum;

Momentum of the machine = - momentum of the ball

MV = - mv

V = -mv/M

= - (0.149×42.6)/54.6 m/s

= - 0.11 m/s.

Hence, the recoil velocity of the machine is 0.11 m/s in opposite direction.

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This question is about the physics of a car's stopping distance and the effect of reaction time on it.

The subject of this question is Physics and it is appropriate for high school level students.

In this scenario, the driver is traveling at a speed of 25m/s when they see a hole 55m ahead of them. Since their reaction time is zero, meaning they immediately apply the brakes, the total displacement during the reaction time is 15.0m greater than if they reacted instantly. The stopping distance, in this case, would be the same for both dry and wet concrete, so we need to calculate the distance the car travels during the reaction time and add that to the stopping distance.

To summarize, this question is about the physics of a car's stopping distance and the effect of reaction time on it.

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Answer:

Explanation:

A protostar forms once the nebular cloud condenses and the core begins HEAT.

A protostar is a very young star that is still gathering mass from its parent molecular cloud. The protostellar phase is the earliest one in the process of stellar evolution. A protostar is the earliest stage in star formation in the universe.  When the gas cloud begins to collapse on its own weight, the core begins to heat up. The heat is due to the force of compression of the dust and gas under its gravity. When the pressure and temperatures become high enough, the hydrogen in the core begins to fuse.

It is given that,

Speed of Barbara w.r.t ground, [tex]v_b=-5.9\ m/s[/tex] ( in south)

Speed of neil w.r.t ground, [tex]v_n=-1.4\ m/s[/tex] ( in west)

So, Neil's velocity as seen by Barbara is :

[tex]v^2=\sqrt{(1.4\ m/s)^2+(5.9\ m/s)^2}[/tex]

[tex]v=6.06\ m/s[/tex]

Direction relative to due wet is :

[tex]tan\theta=\dfrac{5.9\ m}{1.4\ m}[/tex]

[tex]\theta=tan^{-1} (4.21)[/tex]

[tex]\theta=76.6\ ^0[/tex]

So, with respect to barbara, Neil is travelling with velocity of 6.06 m/s making an angle of [tex]76.6^0[/tex] due west.

Hence, this is the required solution.

The initial speed of the long jumper is calculated by finding the upward component of her velocity caused by her jumping at a 20-degree angle and achieving a maximum height of 0.6 m, then determining the total velocity by dividing this by the sine of the launch angle. The distance of her jump is found by applying these values in the formula for the range of a projectile. Both calculations assume no air resistance.

In this problem, the initial speed of the jumper is determined using the physics concepts of projectile motion.

To find the initial speed, first, we compute the upward component of the velocity using the formula ਙ = √(2*g*h), where g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the maximum height (in this case, 0.6 m). The upward component of the velocity comes out to be approximately 3.443 m/s.

Second, we determine the initial speed by dividing the upward component of the velocity by the sine of the angle, which in this case is 20 degrees. This gives us an initial speed of approximately 10 m/s.

The distance of the jump (or the range of the projectile) can be calculated using the formula R = (vₒ²/g) * sin(2θ), where R is the range, vₒ is the initial velocity, g is the acceleration due to gravity, and θ is the launch angle. Substituting the values, the range comes out to be approximately 6.59 m.

These answers are based on ignoring any effects of air resistance.

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The actual car is 5.46 meters long.

To determine the length of the actual car based on its scale model, first note the given details:

We can calculate the length of the actual car using the formula:

Length of actual car = (Length of model car in cm) × (Scale factor in meters/cm)

Substituting the given values:

Length of actual car = 18.2 cm × 0.3 meters/cm = 5.46 meters

Thus, the actual car is 5.46 meters long.