At a distance of 40 ft from the pad, a man observes a helicopter taking off from a heliport. If the helicopter lifts off vertically and is rising at a speed of 53 ft/sec when it is at an altitude of 129 ft, how fast is the distance between the helicopter and the man changing at that instant

Answers

Answer 1

Answer:

The distance between the helicopter and the man is increasing at a rate of 50.622 feet per second.

Explanation:

First, we create a geometric diagram representing the situation between man (point O),  helicopter (point P) and helipad (point H). The distance between man and helicopter is represented by Pythagorean Theorem:

[tex]x^{2}+y^{2} = r^{2}[/tex] (1)

Where:

[tex]x[/tex] - Distance between man and helipad, in feet.

[tex]y[/tex] - Distance between helipad and helicopter, in feet.

[tex]r[/tex] - Distance between man and helicopter, in feet.

By Differential Calculus, we derive an expression for the rate of change of the distance between man and helicopter ([tex]\dot r[/tex]), in feet per second:

[tex]2\cdot x\cdot \dot x + 2\cdot y\cdot \dot y = 2\cdot r\cdot \dot r[/tex]

[tex]\dot r = \frac{x\cdot \dot x + y\cdot \dot y}{r}[/tex]

[tex]\dot r = \frac{x\cdot \dot x + y\cdot \dot y}{\sqrt{x^{2}+y^{2}}}[/tex] (2)

Where:

[tex]\dot x[/tex] - Rate of change of the distance between man and helipad, in feet per second.

[tex]\dot y[/tex] - Rate of change of the distance between helicopter and helipad, in feet per second.

If we know that [tex]x = 40\,ft[/tex], [tex]y = 129\,ft[/tex], [tex]\dot x = 0\,\frac{ft}{s}[/tex] and [tex]\dot y = 53\,\frac{ft}{s}[/tex], then the rate of change of the distance between man and helicopter is:

[tex]\dot r = \frac{x\cdot \dot x + y\cdot \dot y}{\sqrt{x^{2}+y^{2}}}[/tex]

[tex]\dot r = 50.622\,\frac{ft}{s}[/tex]

The distance between the helicopter and the man is increasing at a rate of 50.622 feet per second.

At A Distance Of 40 Ft From The Pad, A Man Observes A Helicopter Taking Off From A Heliport. If The Helicopter

Related Questions

What is the magnitude and direction of the net force on a ball that has a force of 27N North and 18N North applied to it?

Answers

Answer:

Magnitude: =  32.45 Direction: =  33.69

Explanation:

The magnitude of the net force acting on an object is equal to the mass of the object multiplied by the acceleration of the object, as shown in this formula. We find its magnitude using the Pythagorean Theorem or the distance formula, and we find its direction using the inverse tangent function. Given a position vector →v=⟨a,b⟩, the magnitude is found by |v|=√a2+b2. The direction is equal to the angle formed with the x-axis, or with the y-axis, depending on the application.

What is the flux through the plane taken parnllel to the field?​

Answers

Answer:

the flux through the plane is zero.

Explanation:

A 20-kg child is on top of a slide was pushed down by his brother giving him an initial speed of 2 m/s down the slide. what is the child's speed at the bottom of the slide if the slide is 5 m high and 10m long and the force of friction between the child and slide is negligible?​

Answers

Answer:

please find your answer in the attached picture, along with explanation.

You are riding on a carousel that is rotating at a constant 24 rpm. It has an inside radius of 4 ftand outside radius of 12 ft. You begin to run from the inside to the outside along a radius. Your peak velocity with respect to the carousel is 6 mph and occurs at a radius of 8 ft.What are your maximum Coriolis acceleration magnitude and its directionwith respect to the carousel

Answers

Answer:

magnitude of the Coriolis acceleration is 44.235 ft/s² and the direction of the acceleration is along the axis of transmission

Explanation:

Given the data in the question;

Speed of carousel N = 24 rpm

From the diagram below, selected path direction defines the Axis of slip.

Hence, The Coriolis is acting along the axis of transmission

Now, we determine the angular speed ω of the carousel.

ω = 2πN / 60

we substitute in the value of N

ω = (2π × 24) / 60

ω = 2.5133 rad/s

Next, we convert the given velocity from mph to ft/s

we know that; 1 mph = 1.4667 ft/s

so

[tex]V_{slip[/tex] = 6 mph = ( 6 × 1.4667 ) = 8.8002 ft/s

Now, we determine the magnitude of the Coriolis acceleration

[tex]a_c[/tex] = 2( [tex]V_{slip[/tex] × ω )

we substitute

[tex]a_c[/tex] = 2( 8.8002 ft/s × 2.5133 rad/s )

[tex]a_c[/tex] = 44.235 ft/s²

Hence, magnitude of the Coriolis acceleration is 44.235 ft/s² and the direction of the acceleration is along the axis of transmission

1.What is the Kinetic energy of a 3 kg object moving at 4 m/s?
Plz help I’ll give points

Answers

Answer:

24 J

Explanation:

[tex]K = \frac{1}{2} mv^{2} = \frac{1}{2} (3kg)(4m/s)^{2} = 24 J[/tex]

give 3 example of right quantities that have no unit​

Answers

Answer:

velocity ratio

mechanical advantage

Relative density

A ball bounces changing velocity from vi=15m/s[D] to vf=15m/s[U] in t=0.01s. The balls acceleration is *
A) 0
B) 30m/s/s
C) 3000m/s/s
D) 0.3m/s/s

Answers

Answer:

Option (A) is correct

Explanation:

a= (vf-vi)/ t

put the values

hence,

a= ( 15-15)/0.01

a=0

how do stocks and bonds differ

Answers

Answer:

Explanation:

Stocks give you partial ownership in a corporation, while bonds are a loan from you to a company or government. The biggest difference between them is how they generate profit: stocks must appreciate in value and be sold later on the stock market, while most bonds pay fixed interest over time.

Answer:

Stocks give you partial ownership in a corporation, while bonds are a loan from you to a company or government. The biggest difference between them is how they generate profit: stocks must appreciate in value and be sold later on the stock market, while most bonds pay fixed interest over time.

Explanation:

None

Can someone please help me on this?

Answers

Don’t listen to the link the other person sent!!!

If you weigh 690 N on the earth, what would be your weight on the surface of a neutron star that has the same mass as our sun and a diameter of 15.0 km ? Take the mass of the sun to be ms = 1.99×1030 kg , the gravitational constant to be G = 6.67×10−11 N⋅m2/kg2 , and the free-fall acceleration at the earth's surface to be g = 9.8 m/s2 . Express your weight wstar in newtons.

Answers

Answer:

W' = 1.66 x 10¹⁴ N

Explanation:

First, we will calculate the mass:

[tex]W = mg[/tex]

where,

W = weight on earth = 690 N

m = mass = ?

g = acceleration due to gravity on earth = 9.8 m/s²

Therefore,

[tex]m = \frac{W}{g} = \frac{690\ N}{9.8\ m/s^2}\\\\m = 70.4\ kg[/tex]

Now, we will calculate the value of g on the neutron star:

[tex]g' = \frac{GM}{R^2}[/tex]

where,

g' = acceleration due to gravity on the surface of the neutron star = ?

G = Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²

M = Mass of the Neutron Star = 1.99 x 10³⁰ kg

R = Radius of the Neutron Star = 15 km/2 = 7.5 km = 7500 m

Therefore,

[tex]g' = \frac{(6.67\ x\ 10^{-11}\ N.m^2/kg^2)(1.99\ x\ 10^{30}\ kg)}{(7500\ m)^2}\\\\g' = 2.36\ x\ 10^{12}\ m/s^2[/tex]

Therefore, the weight on the surface of the neutron star will be:

[tex]W' = mg'\\W' = (70.4\ kg)(2.36\ x\ 10^{12}\ m/s^2)[/tex]

W' = 1.66 x 10¹⁴ N

What is perihelion and aphelion in short.

Answers

I dont know you could start by asking your teacher, parent, and or siblings.

Ps the last part was a joke they never help.

Answer:

I think that perihelion is the point of the Earth's course that is close to the Sun. And i'm sure that aphelion in short is astronomy or otherwise the point in the orbit of a planet.

Explanation:

Hope this helps :)

This is energy of motion
Hint
First two letters Ki

Answers

Answer: Kinetic Energy

Explanation:Kinetic energy is the energy of motion. All moving objects have kinetic energy.

Answer:

Kinetic energy

Explanation:

Kinetic energy is energy produced when the object is in motion.

A particle oscillates in simple harmonic motion, with amplitude A and period T. The particle starts from position x = A. What is the magnitude of the particle's displacement a time 3T/2?

A. 3A
B. 6A
C. 2A
D. 0

Answers

Answer:

i guess it is D because,

y = A sin(wt)

w = [tex]\frac{2\pi }{T}[/tex] and t = 3T/ 2

now, Y = A sin ( [tex]\frac{2\pi }{T} X \frac{3T}{2}[/tex])

so, Y = 0radian

Explanation:

The magnitude of the particle's displacement a time 3T/2 is zero. The correct option is D.

What is magnitude?

Magnitude is simply "distance or quantity" in the context of physics.

A = amplitude of SHM

T = time period of SHM

At t = 0 s, the position of a particle is, x = A

At t = 3T/2, find the magnitude of the particle's displacement

d = magnitude of displacement of particle at time

t = 3T/2

t = ?

t= t1 + t2 = T + T/2

where

t1 = T

t2 = T/2

Now, in time t1 = T, the particle will return to its initial position as the particle completes one full cycle of motion in time T.

Therefore, after time t1 = T, the position of the particle is given by x = A, and the total displacement by the particle is 0.

Now in time

t2=T/2

The particle will go to another extreme position, given by x = -A.

Therefore, the net displacement of particles in time

3/T2

is given by:

d=0+(−A)=−A

d=−A

Therefore, the correct option is D. 0.

To learn more about the magnitude, refer to the link:

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1. A train is moving north at 5 m/s on a straight track. The engine is causing it to accelerate northward at 2 m/s^2.
How far will it go before it is moving at 20 m/s?
A) 83
B) 43
C) 39
D) 94
E) 20

Answers

Answer:

(D) x = 93.8 m

Explanation:

v^2 = v0^2 + 2ax

(20 m/s)^2 = (5 m/s)^2 + 2(2 m/s^2)x

Solving for x,

x = 93.8 m

A circuit is built based on this circuit diagram.
What is the equivalent resistance of the circuit?
0.61 Ω
Ο 1.6 Ω
7.5Ω
Ο 18 Ω
12V
3.0 Ω.
6.0 Ω
9.Ο Ω.
Will mark brainlyest. No “links” I don’t want them

Answers

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the concept of resistors,

The equivalent circuit is given as,

1/Rp = 1/3 + 1/6 + 1/9

1/Rp = 6+3+2/18

1/Rp = 11/18

Rp = 18/11 ==> 1.63 ==> 1.6 ohms

hence the equivalent resistance of the circuit is 1.6 ohms

The equivalent resistance of the circuit is 1.6Ω. The correct option is B.

What is Ohm’s law?

Ohm’s law state that ” At constant temperature, the current (I) flowing through a conductor is directly proportional to the potential difference(V) across the two endpoints of the given conductor.”

I.e V ∝ I

V=IR

Where V= potential difference across the conductor.

I = current flowing through the conductor.

R= constant pf proportionality i.e resistance which unit is ohm(Ω).

There are two ways we can connect the resistors.

(i) series connection

If a number of resistors are said to be connected in series When the same current (I) flows through them.

Let R1, R2, and R3 be the resistors connected in series.

Then the R equivalent is

Req=R1+R2+R3

(ii) parallel connection

A number of resistors are said to be connected in parallel when the same potential difference(V) exists across each of them.

Let R1, R2, and R3 be the resistors connected in parallel.

Then the R equivalent is

1/Req=1/R1+1/R2+1/R3

In this question,

The three resistance connected in parallel by applying the above formula we get,

1/Req=1/R1+1/R2+1/R3

1/Req = 1/3 + 1/6 + 1/9      .................  (∵R1=3Ω,R2=6Ω AND R3=9Ω)

1/Req =11/18

Req=18/11

Req=1.6363Ω

Req≈1.6Ω

Therefore, The equivalent resistance of the circuit is 1.6Ω.

To learn more about resistance click:

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what is the meaning of love ? ...What is love?​

Answers

Answer:

love is a feeling that you get for people that you care about.

Explanation:

Answer:

Love is a feeling of affection for someone, when you adore somebody.

I wish true love and soul mates were real ( •_•)

The universe cooled after the Big Bang.At some point hydrogen atoms combined to form helium.What is this process called?

Answers

Answer:

Nuclear fusion

Explanation:

Average running speed is 8km/h. Convert this to m/s :
a)8m/s
b)2.2m/s
c)28.8m/s
d)8km/h

Answers

Answer:

Im not sure if you mean miles per hour or meters per hour but if it is miles it is 4.97 miles per hour and if it is meters then it is 8000 meters per hour

Explanation:

Sorry if I'm wrong

An object is pushed with a force of 400 N for 20 meters; what is the work done on the object? Solve using W=F*d

Answers

Answer:

800joules

Explanation:

work is measured in joules

If you were on a spaceship traveling at 0.50c away from a star, what speed
would the starlight pass you?

Answers

Explanation:

The speed of light in vacuum is the same by all observers (2nd Principle). You would find that the starlight passes you at c. This is more than a thousand times faster than existing space craft.

According to all observers, the velocity of light in a vacuum will be the same (2nd Principle). You'd discover that the starlight is passing you at c. Compared to current spacecraft, this really is a thousand times faster.

What is Speed?

The amount of the shift in approach per unit of time or the size of the displacement over time for an object can be used to describe speed, which would be a scalar quantity in everyday language and kinematics.

The maximum speed that can be maintained when a time period grows closer to zero is the starting speed.

By dividing the object's distance traveled by the duration of the interval, the mean pace of the object for the given period of time is calculated. Speed and velocity are not always the same thing.

To know more about Speed:

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A loudspeaker in a parked car is producing sound whose frequency is 20 510 Hz. A healthy young person with normal hearing is standing nearby on the sidewalk but cannot hear the sound because the frequency is too high. When the car is moving, however, this person can hear the sound. (a) Is the car moving toward or away from the person

Answers

Answer:

The car must be moving away from the person.

Explanation:

From Doppler's Effect, we know that when a sound source moves towards a stationary observer, the apparent frequency of that sound increases. While the apparent frequency decreases if the source moves away from the stationary observer.

The audible range of frequencies for a human ear is 20 Hz to 20000 Hz. Therefore, in order for the sound of a loud speaker to be audible for the person, the frequency must decrease below 20000 Hz.

Due to this reason, the car must be moving away from the person.

can someone please help me answer this!!

Answers

i may be wrong, but i believe it is C, as there is no mention of sunlight being a control variable. the amount of sunlight greatly determines plant growth since they obviously use it for photosynthesis

You and your friends are pushing a car with a total of 1080 N of force. You are able to push the car for a distance of 218 m. Calculate the work done on the car.

Answers

Answer:

How much power is required to pull a sled if you use 60J of work in 5 seconds? ... Misfortune occurs and Renatta and her friends find themselves getting a workout. They apply a cumulative force of 1080 N to push their car 218 m to the ... Calculate the amount of work done when moving a 567N crate a distance of 20 meters.

Explanation:

Misfortune occurs and Renatta and her friends find themselves getting a ... They apply a cumulative force of 1080 N to push the car 218 m to the nearest fuel ... Write down what they give you. ... Determine the work done by Lamar in deadlifting 300 kg to a height of 0.90 m ... Work = Force x Distance = Joules (force = weight).

8. What is the mass and charge of a proton?
A. 1 amu, no charge
B. 1 amu, charge of +1
C. Mass of O, charge of -1
D. None of the above

Answers


B.

Step By Step Explanation:

Which electromagnetic wave has the shortest wavelength?



Which electromagnetic wave would have a wavelength approximately the size of the tip of a pencil?



Which electromagnetic wave has the longest wavelength?

Answers

Answer:

shortest - gamma Ray's

size of a pencil tip : most likely microwaves

longest - radio waves

Gamma rays have the shortest wavelength whereas Radio waves have the longest wavelength. The wave whose wavelength is about the size of the tip of a pencil is infrared ray.

What is an Electromagnetic spectrum?

The whole electromagnetic waves are divided into several classes based on their frequencies or energies as follows, in the order of increasing frequency:

Radio waves

Microwaves

Infrared

Visible

Ultraviolet

X-rays

Gamma rays

The Gamma rays are the shortest wavelength group with frequencies greater than 3 × 10²⁰ Hz.

The Radio waves are the longest wavelength group. Their frequency is lower than 3 × 10⁷ Hz.

The tip of a pencil is about 0.5mm in width.

Calculate the frequency of the wave whose wavelength is about the size of the tip of a pencil i.e. λ = 0.5 mm,

ν = 3×10⁸/(0.5×10⁻³) = 6×10¹¹ Hz.

The infrared rays have frequencies in the range of 3×10¹¹ Hz to 3×10¹³ Hz. So, the wave is infrared.

Infrared waves have a wavelength about the tip of a pencil.

Learn more about the electromagnetic spectrum here

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The first extra-solar planet around a main sequence star (i.e., not a neutron star or white dwarf) was found around the star 51 Pegasi in 1995. The large planet causes a measureable motion of the star around the center of mass of the system. Pegasi 51's orbital motion had a period of 4 days indicating a very large planet very close to the star. A large planet of mass M around a small star of mass 4M. The distance between planet and star is L. Both the planet and star will orbit around the center of mass of the system (marked by the red X).

Required:
Where is the center of mass of the star-planet system?

Answers

Answer:

   [tex]r_{cm}[/tex]= 1/5 L

Explanation:

To find the center of mass of the system let's use

        [tex]r_{cm} = \frac{1}{M}[/tex] ∑ r_i x_i

where m is the total mass of the system

let's apply this expression to our case

       

Let's set the reference frame on the star

         [tex]r_{cm} = \frac{1}{M +4M} ( 4M 0 + M L)[/tex]

         r_{cm} = [tex]\frac{1}{5}[/tex] L

         [tex]r_{cm}[/tex]= 1/5 L

Hey, the breast center is 1/5 of the distance between the star and the planet.

Which category best describes this group of shapes? rhombuses rectangles parallelograms squares II​

Answers

they're parallelograms

a boat carving people more than its capacity is at risk of sinking, why?​

Answers

Answer:

Explained below.

Explanation:

For a boat or any object to float on water, it's density must be less than that of water.

Now, when the maximum capacity of people to be carried by the boat is exceeded, it's possible that the maximum mass of people will also be exceeded depending on the mass of the people in the boat.

Now, we know that; density = mass/volume.

Thus, the higher the mass of the people, the higher the density and the higher the density, the more likely it is to be above that of water and the more likely it is to sink.

A marble and a basketball are rolling toward you at the same velocity. If the same amount of force is used to stop both objects, what is true about the amount of time needed to stop those objects?

Answers

Answer:

The amount of time needed to stop the marble is much less than the amount of time needed to stop the basketball.

Explanation:

To explain this question we can use the equation:

Change in momentum = Force x Time

Where momentum = mass x Velocity

In the case of the basketball, it has a much larger mass than the marble, meaning it has much more momentum than the marble. This means that with the same amount of force, it will need much more time to stop.

Likewise, the marble has less mass than the basketball meaning it will have less momentum. This means that with the same amount of force, it will require less time to stop.

Logically this also makes sense if we think about it in a real life scenario. If we try to stop a marble with our finger, we can stop it much faster then if we try to stop a basketball with our finger because of the difference in mass between the two objects, therefore the marble will require much less time to be stopped than the basketball.

Hope this helped!

A doorknob is a type of wheel and axle. In a doorknob, the door handle acts as the wheel. The handle is connected to a cylinder, called a spindle, which acts as the axle. When the handle turns, the spindle turns in the same direction. The spindle is located inside the handle and pulls the latch back and forth, allowing the door to open.


In the doorknob shown above, when the handle is rotated a distance of 84 millimeters, the spindle is rotated a distance of 14 millimeters. What is the mechanical advantage of this doorknob?
A. 504
B. 6
C. 84
D. 14

Answers

I’m not 100% sure but I believe it’s C.84
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