HELP
Find the value of each calculation, rounded to the correct number of significant figures.


15.2÷4.368=

Area and Speed are derived Units Because they are derived from the Fundamental Units

By proceeding using the dimensional analysis,

We can see,

Area = Length of object x Breadth of object

As we know, both the length and the breadth of the object are measured as Meter(M),

Area = M x M

Now, for Speed,

Speed = distance/time

unit of distance is Meter(M) and unit of time is Second(S), both of these are fundamental quantities.

Speed = Meter/second

Speed = M/S

As we can see, the unit of area is a composition of a fundamental unit and speed is also a composition of fundamental unit and any unit which is composition of one or more fundamental unit is called derived Unit.

Hence it is proved that Area and Speed are Derived Units.

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The perimeter of the pool is measured as 30 feet.

We know that a rectangle is a four sided polygon recall that a polygon is any figure that has n sides. The number of sides in a  polygon could move from three to infinity. The polygons come in different shapes and are solids with definite values of surface areas and volumes.

The rectangle is four sided which each of the angles of the rectangle adding up to give 360 degrees. It must be noted that the opposite sides of the rectangle are equal to each other.

We have the following information;

Length of the pool = 4(3 feet) = 12 feet

Width of the pool = 3 feet

Since perimeter = 2 ( length + width)

Perimeter = 2( 12 + 3)

Perimeter = 30 feet

Hence, the perimeter of the pool is measured as 30 feet.

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The final velocity of the plane at the end of the railway is:

V2f=v2i+2a(x)

v2f=(55m/s)2−(2)(2.5m/s2)(600m)

vf=5m/s.

Since the final velocity is not equal to zero, the plane would not be able to stop at the end of the runway.

Technically, there may be the most effective manner for the aircraft to stay putting motionless inside the air if weight and raise cancel every other out perfectly, and at the equal time thrust and drag cancel every different out too. but this is exceptionally uncommon. To live within the air and sustain its flight, a plane wishes to be moving forward.

In addition to wing spoilers, airplanes use disc brakes. aircraft disc brakes are just like the braking system in automobiles. They consist of a pair of calipers that, while engaged, squeeze pads towards the rotors of an aircraft's landing gear. Disc brakes are designed to stay static at all times. maximum planes use a long runway earlier than takeoff to gain enough velocity for the aircraft to raise up into the air. most airplanes can take off handiest if they are moving rapidly sufficient.

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Answer:

[tex]62.5[\frac{km}{h}][/tex]

Explanation:

if the required speed is 's', then it is possible to make up the next equation:

[tex]\frac{100}{8} =\frac{s}{5};[/tex]

finally,

s=100*5/8=62.5 [km/h].

The lenght of the missing side is 29.41 ft.

To calculate the missing length of the triangle, we use pythagoras theorem.

Pythagoras theorem states that in a right angle triangle, the square the hypotenus is equal to the sum of the square of the two other sides.

These can be expressed mathematically as

From the question,

Substitute these values into equation 1

Hence, the lenght of the missing side is 29.41 ft.

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The magnitude of velocity of the ball dropped from a 91 m tall building at the point of impact is 42.8 m / s

s = ut + 1 / 2 at²

a = v / t

s = Distance

u =Initial velocity

a = Acceleration

t = Time

s = 91 m

a = 10 m / s²

s = ut + 1 / 2 at²

91 = 0 + ( 1 / 2 * 10 * t² )

t = √ ( 18.2 )

t = 4.27 s

v = 10 * 4.27

v = 42.7 m / s

The position-time graph and the velocity-time graph that represents the problem is drawn in the image attached.

Therefore, the magnitude of velocity of the ball is 42.7 m / s

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a. Her x position at t = 0.80 s is 0.0832 m

b. Her y position at t = 0.80 s is -28.8 m

c. Her x velocity component at t = 0.80s is 2.08 m/s

d. her y velocity component at t = 0.80s is -3.6 m/s

Since the skateboarder travels on a horizontal surface with an initial velocity of 3.6 m/s toward the south and a constant acceleration of 2.6 m/s² toward the east.

Now since she starts from the origin, to find her x position after 0.80 s, using the equation of motion for the x - components of motion,

x = ut + 1/2at² where

So, substituting the values of the variables into the equation, we have

x = ut + 1/2at²

x = 0 m/s × 0.8 s + 1/2 × 2.6 m/s² × (0.8 s)²

x = 0 m + 1.3 m/s² × 0.64 s²

x = 0 m + 0.832 m

x = 0.832 m

So, her x position at t = 0.80 s is 0.0832 m

Using the equation of motion for her y - components of motion, her y position is y = ut + 1/2at² where

So, substituting the values of the variables into the equation, we have

y = ut + 1/2at²

y = -3.6 m/s × 0.8 s + 1/2 × 0 m/s² × (0.8 s)²

y = -3.6 m × 0.8 s + 0

y = -28.8 m

So, her y position at t = 0.80 s is -28.8 m

Using the equation of motion for her x - component of motion, her x velocity compoent after t = 0.8 s is

v = u + at where

So, we have

v = u + at

v = 0 m/s + 2.6 m/s² × 0.8 s

v = 0 m/s + 2.08 m/s

v = 2.08 m/s

So, her x velocity component at t = 0.80s is 2.08 m/s

Using the equation of motion for her y - component of motion, her xyvelocity compoent after t = 0.8 s is

v = u + at where

So, we have

v = u + at

v = -3.6 m/s + 0 m/s² × 0.8 s

v = -3.6 m/s + 0 m/s

v = -3.6 m/s

So, her y velocity component at t = 0.80s is -3.6 m/s

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The distance covered by the runner after starting from rest is 39.74 m/s².

The real route length of a moving particle or object is referred to as distance. The shortest distance between a body's initial and final positions is referred to as displacement. Speed is the amount of distance a particle travels in one unit of time.

The constant acceleration of a runner is 1.1 m/s².

The runner maintains the constant acceleration for 8.5 seconds.

So,

a = 1.1 m/s²

t = 8.4 seconds

Since the runner starts from the rest.

Therefore, the initial velocity u = 0 m/s

Using the equation of motion,

s = ut + (1/2) × a × t²

s = 0 × 8.5 + ( 1/2 ) × 1.1 × 8.5 × 8.5

s = ( 1/2 ) × 79.475

s = 39.737 m/s²

s = 39.74 m/s²

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Answer:

B

Explanation:

The balancing level that we are when standing at a normal posture is the Normal balancing level. That is option D.

Posture is defined as the bearing of one's body while at rest or while moving.

Normal posture can be defined as the normal position of the body while standing which involves standing straight and tall with shoulders back and the hands by the sides with the head kept in line with the body level.

The balancing level of posture is that level where the body is being positioned in such a manner as to reduce the amount of work done by the muscles.

Therefore, the balancing level that we are when standing at a normal posture is the Normal balancing level.

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The mass of the second rocket should be 0.4 kg in order for the acceleration to be half of the first rocket's acceleration.

We know that,

F = m a

where,

F = Force

m = Mass

a = Acceleration

Given that,

[tex]F_{1}[/tex] = 100 N

[tex]m_{1}[/tex] = 0.2 kg

[tex]F_{1}[/tex] = [tex]F_{2}[/tex] = 100 N

[tex]a_{2}[/tex] = [tex]a_{1}[/tex] / 2

[tex]F_{1}[/tex] = [tex]m_{1}[/tex] *  [tex]a_{1}[/tex]

[tex]a_{1}[/tex] = 100 / 0.2

[tex]a_{1}[/tex] = 500 m / s²

[tex]a_{2}[/tex] = 500 / 2

[tex]a_{2}[/tex] = 250 m / s²

[tex]m_{2}[/tex] = 100 / 250

[tex]m_{2}[/tex] = 0.4 kg

According to Newton's second law of motion, acceleration of an object is the result of force acting on the object.

Therefore, The mass of the second rocket should be 0.4 kg

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Answer:

The electrostatic interactive force between electrical charges is exactly the same as the gravitational interaction between them

Explanation:

The magnitude of charge is independent of the weight and displacement of the charge but only sign of the charge is the dependent factor.

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Answer:

Assuming the height at which the wrench was dropped is 336 feet,

the person will hear the sound in 0.3 sec and the wrench will hit the ground only after 4.58 seconds so there is enough time to get out of the way

Explanation:

Without knowing the exact height at which the 24th floor is located, it would be difficult to determine whether the wrench will hit the ground before the sound hits the ground

Realistically, we can assume each floor of the building is 14' high

So the height at which the 24th floor is located is 24 x 14 = 336 feet

To travel 336 feet at 1100 feet per second, sound will take 336/1100 seconds which is 0.30 second

Let's compute the time taken for the wrench to hit the ground

The acceleration due to gravity is usually taken to be 16 feet/second²

The displacement which is the distance traveled by an object with an initial velocity of u in time t is given by the equation:
s = ut + (1/2)t²

Here the initial velocity is 0

So the equation is
s = 1/2 x 32 x t² = 16t²

To cover 336 feet we substitute 336 for s and get

336 = 16t²

t² = 336/16

t = ±√(336/16) ≈ 4.58 seconds (we only take the positive root)

So the person will hear the sound in 0.3 sec and the wrench will hit the ground only after 4.58 seconds so there is enough time to get out of the way

In general, we can state that if the height from which the wrench was dropped is h then time t taken for wrench too hit the ground is

t = √(h/16) seconds

If this is greater than the time taken for sound to travel the same distance then the person can get out of the way

Answer:

2g cube of Aluminum

Explanation:

The total heat supplied by the plant to convert the water to steam is 596.7 kcal.

Heat capacity is the quantity of heat required to raise the temperature of entire mass of a substance.

Q = Heat supplied to the water to the boiling point + Heat supplied to vaporize the water.

Q = mc₁Δθ + mc₂Δθ + mLv

where;

Substitute the given parameters and solve for the heat supplied in the process.

Q = (1)(1)(100 - 58.6) + (1)(0.48)(131.8 - 100)  + 540(1)

Q = 41.4 + 15.264 + 540

Q = 596.7 kcal

Thus, the total heat supplied by the plant to convert the water to steam is 596.7 kcal.

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The height of the cliff from the ground is 19.6 meters.

Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration due to gravity.

Given is the initial speed of soccer ball kicked horizontally off a cliff which is 8 m/s. It cover a horizontal distance of 16 m. From this, we can write -

Horizontal initial velocity = u [h] = 8m/s

Horizontal distance covered = S [h] = 16m

For horizontal direction, of motion, we can write -

u [h] = 8m/s

S [h] = 16m

From second equation of motion applied for the horizontal direction -

S[h] = u[h] x t + 1/2 a[h] x t²

Since horizontal acceleration a[h] is zero, we can write -

t = S[h]/u[h]

t = 16/8

t = 2 seconds

Since the ball is kicked horizontally, the initial vertical velocity u[v] will be 0 m/s.

The acceleration in the vertical direction a[v] is directed vertically downwards and is equal to 9.8 m/s².

From second equation of motion applied for the vertical direction -

S[v] = u[v] x t + 1/2 x a[v] t²

S[v] = 1/2 x a[v] t²                      {u[v] = 0}

S[v] = 1/2 x 9.8 x 4

S(v) = 9.8 x 2

S[v] = 19.6 m

Therefore, the height of the cliff from the ground is 19.6 meters.

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[ The given question is not complete, the complete question is -

A soccer ball is kicked horizontally off a cliff with an initial speed of 8 m/s and lands 16 m from the base of the cliff: What is the time of flight of the soccer ball? What is the height of the cliff? ]

The metric conversion of the given quantities is determined as

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

The metric conversion of the following quantities is calculated as follows;

5 KL = 5 x 1000 L = 5,000 L

3L = 3 x 1/1000 L = 0.003 KL

4g = 4 x 1/1000 g = 0.004 kg

81 kg = 81 x 1000 g = 81,000 g

52 dg = 52 x 1/10 g = 5.2 g

3 dm = 3 x /10 m = 0.3 m

14 mm = 14 x 1/1000 m = 0.014 m

Thus, the metric conversion of the given quantities is determined as

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The gravitational potential energy of an object depends on  mass of the object, gravitational field and height of the object.

The gravitational potential energy of an object is the energy possessed by the object due to the object's position above the ground level.

P.E = mgh

where;

The factors affecting gravitational potential energy of an object include;

Thus, the gravitational potential energy of an object depends on  mass of the object, gravitational field and height of the object.

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Answer:

d

Explanation:

I remember it was right

The ball rise 18.42 m from its original position.

Height is the vertical distance between two points.

To calculate the height of the ball, from the original position, we use the formula below.

Formula:

Make h the subject of the equation

Where:

From the question,

Substitute these values into equation 2

Hence, the ball rise 18.42 m from its original position.

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An auto's velocity increases uniformly from 6.0 m/s to 20 m/s while covering 70 m in a straight line, its acceleration is 2.6 [tex]m/s^2\\[/tex] and the time taken is 5.4 s.

The probable rate at which an object’s velocity changes with respect to time is referred to as its acceleration in mechanics. They are vector quantities and accelerations.

The direction of the net force acting on an object determines the direction of its acceleration.

The meter per second ([tex]m/s^2\\[/tex]) unit of acceleration is used to measure speed. The square meter is a measure of area ([tex]m^2[/tex])

The auto's velocity increases uniformly from 6m/s to 20m/s while it is covering the total of 70m.

Since it increases uniformly, thus we can use equation of motion

[tex]V^2 - U^2 =2as[/tex]

U = 6m/s

V = 20m/s

s = 70 m

Thus,

[tex](20)^2 - (6)^2 = 2*a*70[/tex]

a = 2.6 [tex]m/s^2\\[/tex]

Then for the time, we have

a = [tex]\frac{(V-U)}{t}[/tex]

2.6 = [tex]\frac{20 - 6}{t}[/tex]

t = 5.4 s

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If a person swims at a constant speed of 1 meter per second, than the linear function will be used to model the distance travelled by the swimmer.

The parent function is "the principal's of ice"

A linear function is a function that forms a straight line on a graph. It is generally a polynomial function whose degree is at most 1 or 0. Although linear functions are also represented in terms of calculus and linear algebra.

Here Y-axis represents Distance and X-axis represents Time.

Also speed is the rate of change of distance with respect to time i.e. distance is changing linearly with time

Mathematically it is  [tex]Speed = \frac{distance}{time}[/tex].

Change in Distance = Change in time and hence speed is constant.

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The rocket ship rises to a height of 27.83 km above the launch pad after 94 seconds of flight.

We know that,

s = u t + 1 / 2 a t²

where,

s = Displacement

u = Initial velocity

a = Acceleration

t = Time

Given that,

u = 0

a = 6.3 m / s²

t = 94 s

s = 0 + 1 / 2 ( 6.3 * 94² )

s = 27833.4 m

s = 27.83 km

Displacement the distance between the initial point and final point. It is denoted using s.  

Therefore, the rocket ship rises to a height of 27.83 km above the launch pad after 94 seconds of flight.

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Force = (mass) x (acceleration)

so

Acceleration = Force / mass

Acceleration = (1400 N) / (70 kg)

Acceleration = 20 m/s²

The characteristic that is used to measure light radiated by a star is luminosity. The correct option is C.

The radiant power emitted by a light-emitting object with respect to time is measured as luminosity, which is an absolute measure of radiated electromagnetic power.

The total amount of electromagnetic energy radiated per unit of time by a star, cosmos, or other celestial object is referred to as luminosity in astronomy.

The amount of light emitted by a star is measured using luminosity. It is the total amount of emery or light emitted by a star per unit of time. Or it is the total energy produced by a star in one second from its surface.

Thus, the correct option is C.

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Your question seems incomplete, the missing options are:

Size

color

luminosity

temperature

There are few points given to us in this question.

A) There are 1.41× 10^16 m in 1.5 light years

B) There are 9.4 × 10^4 AU in 1.5 light years

What is a light year?

Many might confuse it with time because of the presence of term “year” this term is actually used for space objects to measure distance. Light Year is the distance travelled by light in one Earth year.

It’s a term named by German scientist Friedrich Bessel who first used it in 1838.

One light year is about 6 trillion miles or 9.46 trillion kilometers.

To solve part A, we will first multiply V(light) with time (in seconds) in a year and multiply the product with 1.5 light year per light year.

Now let us understand what is Astronomical Unit AU?

AU is also used to measure distance but within our solar system. It is usually the average distance between Sun and Earth. It is about 93 million miles or 150 million kilometers.

To solve part B, we first convert the light year to AU and we do this by using the final value from part A and then convert it in significant figure to obtain a proper value for the answer.

The calculations are shown in the figures below.

Hence,

A) There are 1.41× 10^16 m in 1.5 light years

B) There are 9.4 × 10^4 AU in 1.5 light years

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The person must climb the stairs about eight times.

We know that energy is the ability to do work. Work and energy are two quantities that are dimensionally similar to each other. In this case, we are trying to obtain the number of times that A 100.0 kg person will need to climb a 10.0 m stairway how many times to "work off" each excess 20 Cal (kcal) consumed.

Now;

Work done by the person = mgh =  100.0 kg  * 10 m/s^2 * 10 m = 10000 J

To convert from joules to kcal, we know that;

1 kcal = 4184 J

x =  10000 J

x = 1 kcal *  10000 J/4184 J

x = 2.39 kcal

In order to burn off the excess calories, the person must climb the stairs;

20 kcal/2.39 kcal = 8

The person must climb the stairs about eight times.

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The speed of the archer is 0.15m/s

The weight of the arrow compared to the man is

60/0.03 = 2000.

Thus, the man is 2000x heavier than the arrow.

Momentum is defined as P = m v or mass times velocity.

This must always be conserved. Since they stand at rest, the total momentum is zero.

The momentum of the arrow once shot is

50 x 0.03,

and thus the momentum of the archer is given by

60 x speed = 50 x 0.03

This rearranges into speed = (50 x 0.03) / 60

=0.15m/s

The speed of the archer is

=(speed of the arrow x mass of the arrow) / mass of the archer

=(50 × 0.030)/60

=0.15m/s

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