A kayak on a lake is moving at a constant speed of 4.1 m/s in a direction 41.6° north of west. After 10 min, find the following.(a) how far west the kayak has traveled km (b) how far north the kayak has traveled km

Answer:

merry go round and Ferris wheel have a constant acceleration due to the change in direction at every point.

Answer:

A merry-go-round is accelerating. Acceleration is a change in speed, direction, or both. Even though the speed of the merry-go-round does not change, its direction constantly changes as it spins.

Explanation:

Answer:

[tex]28\; \rm m \cdot s^{-1}[/tex].

Explanation:

Apply the SUVAT equation [tex]\left(v^2 - u^2) = 2\, a \, x[/tex], where:

Assume that going downwards corresponds to a positive displacement. For this question:

Solve this equation for [tex]v[/tex]:

[tex]\displaystyle v = \sqrt{2\, a\, x + u^2} = \sqrt{2\times 9.8 \times 40} = 28\; \rm m \cdot s^{-1}[/tex].

In other words, the rock reached a velocity of [tex]28\; \rm m\cdot s^{-1}[/tex] (downwards) right before it hits the ground.

Let [tex]v[/tex] be the velocity (in [tex]\rm m \cdot s^{-1}[/tex]) of this rock right before it hits the ground. Under the assumptions of this question, it would take a time of [tex]t = (v / 9.8)[/tex] seconds for this rock to reach that velocity if it started from rest and accelerated at [tex]9.8\; \rm m \cdot s^{-2}[/tex].

Note that under these assumptions, the acceleration of this rock is constant. Therefore, the average velocity of this rock would be exactly one-half the sum of the initial and final velocity. In other words, if [tex]u[/tex] denotes the initial velocity of this rock, the average velocity of this rock during the fall would be:

[tex]\displaystyle \frac{u + v}{2}[/tex].

On the other hand, [tex]u = 0[/tex] because this stone is released from rest. Therefore, the average velocity of this rock during the fall would be exactly [tex](v / 2)[/tex].

The displacement of an object over a period of time is equal to the length of that period times the average velocity over that period. For this rock, the length of this fall would be [tex]t = (v / 9.8)[/tex], while the average velocity over that period would be [tex](v / 2)[/tex]. Therefore, the displacement (in meters) of the rock during the entire fall would be:

[tex]\displaystyle \left(\frac{v}{2}\right) \cdot \left(\frac{v}{9.8}\right) = \frac{v^2}{19.6}[/tex].

That displacement should be equal to the change in the height of the rock, [tex]40\; \rm m[/tex]:

[tex]\displaystyle \frac{v^2}{19.6} = 40[/tex].

Solve for [tex]v[/tex]:

[tex]v = 28\; \rm m \cdot s^{-1}[/tex].

Once again, the speed of the rock would be [tex]28\;\rm m \cdot s^{-1}[/tex] right before it hits the ground.

Explanation:

It is given that,

Mass of a bungee jumper is 65 kg

The time period of the oscillation is 38 s, hitting a low point eight more times.It means its time period is

[tex]T=\dfrac{38}{8}\\\\T=4.75\ s[/tex]

After many oscillations, he finally comes to rest 25.0 m below the level of the bridge.

For an oscillating object, the time period is given by :

[tex]T=2\pi \sqrt{\dfrac{m}{k}}[/tex]

k = spring stiffness constant

So,

[tex]k=\dfrac{4\pi ^2m}{T^2}\\\\k=\dfrac{4\pi ^2\times 65}{(4.75)^2}\\\\k=113.43\ N/m[/tex]

When the cord is in air,

mg=kx

x = the extension in the cord

[tex]x=\dfrac{mg}{k}\\\\x=\dfrac{65\times 9.8}{113.6}\\\\x=5.6\ m[/tex]

So, the unstretched length of the bungee cord is equal to 25 m - 5.6 m = 19.4 m

The spring stiffness constant is 116.7 N/m and the the unstretched length of the bungee cord is 19.54 m.

The given parameters;

The period of oscillation of the bungee jumper is calculated as follows;

[tex]T = \frac{t}{n} \\\\T = \frac{38}{8} \\\\T = 4.75 \ s[/tex]

The spring stiffness constant is calculated as follows;

[tex]T = 2\pi \sqrt{\frac{m}{k} } \\\\\sqrt{\frac{m}{k} } = \frac{T}{2\pi} \\\\k = m \times \frac{T^2}{4\pi^2} \\\\k = 65 \times \frac{(4.75)^2}{4\pi ^2} \\\\k = 116.7 \ N/m[/tex]

The extension of the cord is calculated as follows;

[tex]F = kx\\\\mg = kx\\\\x = \frac{mg}{k} \\\\x = \frac{65 \times 9.8}{116.7} \\\\x = 5.46 \ m[/tex]

The unstretched length of the bungee cord is calculated as;

[tex]\Delta x = l_2-l_1\\\\l_1 = l_2 - \Delta x\\\\l_1 = 25 - 5.46\\\\l_1 = 19.54 \ m[/tex]

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Answer:

(A) 1.43secs

(B) -2.50m/s^2

Explanation:

A commuter backs her car out of her garage with an acceleration of 1.40m/s^2

(A) When the speed is 2.00m/s then, the time can be calculated as follows

t= Vf-Vo/a

The values given are a= 1.40m/s^2 , Vf= 2.00m/s, Vo= 0

= 2.00-0/1.40

= 2.00/1.40

= 1.43secs

(B) The deceleration when the time is 0.800secs can be calculated as follows

a= Vf-Vo/t

= 0-2.00/0.800

= -2.00/0.800

= -2.50m/s^2

Answer:

[tex]$ \frac{4\pi R}{V}$[/tex]

Explanation:

Given :

Mass of ball 1 = m

Mass of ball 2 = 2m

Since, R>>>d, the collision is head on.

Therefore, we get

[tex]$ \frac{v_1 -v_2}{V}=\frac{1}{2}$[/tex]

[tex]$ \therefore \frac{\text{velocity of seperation}}{\text{velocity of approach}}= v_1-v_2 = \frac{V}{2}$[/tex]

Relative velocity is given by V/2. So, we get the time when the masses will again collide as

[tex]$ t = \frac{2\pi R}{\frac{V}{2}}=\frac{4\pi R}{V} $[/tex]

Answer:

Explanation:

The question states that the chairs are spaced 20 m apart through a length of 1 km, or say, 1000 m.

It also does say that each chair weighs 250 kg, and as such the load is

M = 50 * 250

M = 12500.

Taking into consideration, the initial and final heights, we have

h1 = 0, h2 = 200 m

The work needed to raise the chairs,

W = mgh, where h = h2 - h1

W = 12500 * 9.81 * (200 - 0)

W = 2.54*10^7 J

The work is done at a rate of 10 km/h, and at a distance of 1 km, time taken would be

t = 1/10 = 0.1 h or say, 360 s

The power needed thus, is

P = W/t

P = 2.54*10^7 / 360

P = 68125 W, or 68 kW

Initial velocity, u = 0 m/s

Final velocity, v = 10 km/h = 2.78 m/s

Startup time, t is 17 s

Acceleration during the startup then is

a = (v - u)/t

a = 2.78/17

a = 0.163 m/s²

The power needed for the acceleration is

P = ½m [(v² - u²)/t]

P = ½ * 12500 * [2.78²/17]

P = 6250 * 0.455

P = 2844 W

Answer

To get critical pressure

We use

Pc = a/(27b²)

So

= 3.610/(27 X 0.0429²)

We have

= 72.7 atm

Critical temperaturewe

We use

Tc = 8a/27Rb

= 8 x 3.610/(27 x 0.0812 x 0.0429)

= 307 K

Critical volume

We use

Vc =3b =

3 x 0.0429

= 0.129L/mol

Answe

a)  Q = 0.820 10⁻⁹ C ,   b)  Q = -3.52 10⁻⁹ C

Explanation:

The electric field is given by the formula

         E = k q / r²

where E is a vector quantity, so it must be added as a vector

          E_total = E₁ + E₂

let's look for the two electric fields

           E₁ = k q₁ / r₁²

           E₁ = 9 10⁹  5.4 10⁻⁹ / 1.25²

           E₁ = 31.10 N / C

           E2 = k Q / r₂²

           E2 = 9 10⁹ Q / 0.625²

           E2 = 23.04 10⁹ Q N / C           (1)

now we can solve the two cases presented

a) The total field is

            E_total = 50.0 N / C towards + x

since the test charge is positive the electric field E1 points to the right in the direction of the + x axis, so the equation is

            E_total = E1 + E₂

             E₂ = E_toal - E₁

             E₂ = 50.0 -31.10

             E2 = 18.9 N /C

With the value of the electric field we can calculate the charge (Q) using equation 1

             E₂ = 23.04 10⁹ Q

              Q = E₂ / 23.04 10⁹

              Q = 18.9 / 23.04 10⁹

              Q = 0.820 10⁻⁹ C

the charge on Q is positive

b) E_total = -50.0 N / C

              E_total = E₁ + E₂

              E₂ = E_total - E₁

              E2 = -50.0 - 31.10

               E2 = -81.10 N /C

we calculate the charge

             Q = E2 / 23.04 10⁹

             Q = -81.1 / 23.04 10⁹

              Q = -3.52 10⁻⁹ C

for this case the charge is negative

Answer:

it gets colder the higher you go

Answer:

(a) 70cm³

(b) 805 grams

Explanation:

(a) V = L×B×H

= 7cm×5cm×2cm

= 35cm×2cm

= 70cm³

(b) Mass = Volume × Density

= 70cm³ × 11.5g/cm³

= 805 grams

Answer:

-1.17 m/s²

Explanation:

Given:

v₀ = 20 mph = 8.94 m/s

v = 0 m/s

t = 7.63 s

Find: a

v = at + v₀

0 m/s = a (7.63 s) + 8.94 m/s

a = -1.17 m/s²

The acceleration of the plane will be:

"-1.17 m/s²".

According to the question,

Velocity, v₀ = 20 mph or,

                   = 8.94 m/s

and,

                v = 0 m/s

Time, t = 7.63 s

We know the relation,

→ v = at + v₀

By substituting the values,

  0 = a × 7.63 + 8.94

7.63a = - 8.94

      a = -[tex]\frac{8.94}{7.63}[/tex]

         = - 1.17 m/s²  

Thus the response above is correct.

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Answer:

Rutherford

Explanation:

Because

Schrödinger I just took the unit review

Complete question is;

A satellite dish has the shape of a parabola when viewed from the side. The dish is 60 inches wide and 45 inches deep. How far is the receiver from the bottom of the dish if the receiver is placed at the focus?

Answer:

the receiver should be put 40 inches from the bottom of the dish on the concave side of the dish

Explanation:

The base of the dish would simply be the vertex of parabola.

Since we want to find how far the receiver is from the bottom, the place where we'll place the receiver is simply the focus of the parabola.

Now, for example, if this is a parabola that opens upward and has it's vertex at the origin, then half of the diameter at a height of 45 inches gives the two points (60, 22.5) and (-60, 22.5)

Standard form equation of parabola with vertex at origin and pointing upwards is given by;

x² = 4ay

Plugging in the values of x and y gives;

60² = 4a(22.5)

3600/90 = a

a = 40 inches

Thus, the receiver should be put 40 inches from the vertex on the concave side of the dish

Answer:

t=240s

Explanation:

Distance=120m

Acceleration=-5m/s^2

v=0

Let u=x m/s

Using equation v^2-u^2=2as:-

0-x=2(-5)(120)

-x=-1200

x=1200m/s

Using now equation v=u+at:-

0=1200+-5t

5t=1200

t=240s

If a car stops at 120 meters. If it has an acceleration of –5 meters/second², then it would take  6.928 seconds to stop.

The rate of change of the velocity with respect to time is known as the acceleration of the object.

As given in the problem a car stops at 120 meters. If it has an acceleration of –5 meters/second², then we have to find out how long it would take seconds to stop.

By using the second equation of motion,

s = ut + 1/2at²

The distance traveled by car before stopping = 120 meters

acceleration =  –5 meters/second²

-120 = 0 + 0.5×( –5)t²

t² = 120/2.5

t² =48

t = 6.928 seconds

Thus, the time taken by the car before stopping would be 6.928 seconds.

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Explanation:

a. For constant acceleration:

v_avg = ½ (v + v₀)

v_avg = ½ (60 m/s + 15 m/s)

v_avg = 37.5 m/s

b. a = (v − v₀) / t

a = (60 m/s − 15 m/s) / 20 s

a = 2.25 m/s²

c. x = v_avg t

x = (37.5 m/s) (20 s)

x = 750 m

Answer:

[tex]-10 m/s[/tex]

Explanation:

When two cars collide then the momentum of two cars will remains conserved

By momentum conservation equation

               [tex]m1v1i+m2v2i=m1v1f + m2v2f[/tex]

               [tex](100)(8)+(100)(-10)=(100v)+(100)(8)\\ v=-10 m/s[/tex]

12,25 km/h

≈ 3,4 m/s

v = d/t

= 12250m/h

= 12,25km/h

or

v = d/t

= 12250m/h

1h = 60m×60s = 3600s

= 12250m/3600s

≈ 3,4 m/s

Answer:

3.38atm

Explanation:

Using data from the steam table we have that

Moles of water vapour = 907.19 / 18

= 50.4 moles

So

p1 = 30 psi = 30 x 0.68 = 2.04 atm

v1 = 4ft³= 113.2 L

Then from

PV= nRT

Then to find T we use

T1 = p1 V1 / n R

= 2.04 x 113.2 / 50.4 x 0.0821

= 55.8 K

Then to find volume two

v2 = 2v1 + v1

So

3 v1 = 339.6 K

The pressure two we use

P2 = n R T2 / V2

= 50.4 x 0.0821 x 277.6 / 339.6

So we have

= 3.38 atm =

Explanation:

We need to find the value of following expression :

[tex]\dfrac{(6.67 \times 10^{-11})(5.97 \times 10^{24})}{(6.38 \times 10^6)^2}[/tex]

Firstly, solving the numerator of the above expression :

[tex]=\dfrac{39.8199\times 10^{-11+24}}{40.7044\times 10^{12}}\\\\=\dfrac{39.8199\times 10^{13}}{40.7044\times 10^{12}}\\\\=9.7827[/tex]

Rounding off the result = 9.78

In scientific notation : [tex]9.78\times 10^0[/tex]

The value of a = 9.78 and k = 0.

Answer:

a is moving at 60m and the other object

Answer:

46041J

Explanation:

Using Energy lost= mgh

Changing to standard its we have

= 195*1000/3600=54.2m/s

So = 85*54.2*10= 46041J

Answer:

45167.15 J/s

Explanation:

mass of the man = 85 kg

The man's speed = 195 km/h = 195 x 1000/3600 = 54.167 m/s

The man's weight = mg

where

m is the mass

g is acceleration due to gravity = 9.81 m/s^2

weight = 85 x 9.81 = 833.85 N

The rate at which energy is removed from the man = speed x weight

==> 54.167 x 833.85 = 45167.15 J/s

Answer:

v=37.4 m/s

Explanation:

It is given that,

Mass of a ball, m = 3.7 kg

Initial velocity of the ball is u = 8 m/s

We need to find its velocity after 3 seconds. It is moving downwards. The equation of motion is this case is

v=u+gt

[tex]v=8+9.8\times 3\\\\v=37.4\ m/s[/tex]

So, the velocity of the ball after 3 seconds is 37.4 m/s.

Answer:

A) P = 3.3 × 10^(-11) Pa

B) Amplitude of electric field = 1.931 N/C

Amplitude of magnetic field = 6.44 × 10^(-9) T

C) μ_av = 1.65 × 10^(-11) J/m³

D) 50% each for the electric and magnetic field

Explanation:

A) First of all let's calculate intensity.

I = P_av/A

We are given;

P_av = 777 KW = 777,000 W

Distance = 5 km = 5000 m

Thus;

I = 777000/(2π × 5000²)

I = 0.00495 W/m²

Now, the average pressure would be given by the formula;

P = 2I/C

Where C is speed of light = 3 × 10^(8) m/s

P = (2 × 0.00495)/(3 × 10^(8))

P = 3.3 × 10^(-11) Pa

B) Formula for the amplitude of the electric field is gotten from;

E_max = √[2I/(εo•c)].

Where εo is the Permittivity of free space with a constant value of 8.85 × 10^(−12) c²/N.mm²

I and c remain as before.

Thus;

E_max = √[(2 × 0.00495)/(8.85 × 10^(−12) × 3 × 10^(8))]

E_max = √3.72881355932

E_max = 1.931 N/C

Formula for amplitude of magnetic field is gotten from;

B_max = E_max/c

B_max = 1.931/(3 × 10^(8))

B_max = 6.44 × 10^(-9) T

C) Formula for average density is;

μ_av = εo(E_rms)²

Now, E_rms = E_max/√2

Thus;

E_rms = 1.931/√2

μ_av = 8.85 × 10^(−12) × (1.931/√2)²

μ_av = 1.65 × 10^(-11) J/m³

D) The energy density for the electric and magnetic field is the same. So both of them will have 50% of the energy density.

Answer:

The  force is  [tex]F =  1164.6\  lbf[/tex]

The time is   [tex]\Delta t =  2.44 \  s[/tex]

Explanation:

From the question we are told that

  The  mass of the car is  [tex]m  =  2500 \ lbm[/tex]

   The  initial velocity of the car is [tex]u  =  25 \ mi/hr[/tex]

   The final  velocity of the car is  [tex]v  =  50 \  mi/hr[/tex]

  The acceleration is  [tex]a =  15 ft/s^2 =  \frac{15 *  3600^2}{ 5280} =  36818.2 \  mi/h^2[/tex]

Generally the acceleration is mathematically represented as

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

=>   [tex]36818.2 =  \frac{50 - 25 }{ \Delta t}[/tex]

=>   [tex]t = 0.000679 \  hr[/tex]

converting to seconds

       [tex]\Delta t =  0.0000679 *  3600[/tex]

=>     [tex]\Delta t =  2.44 \  s[/tex]

Generally the force is mathematically represented as

        [tex]F  =  m * a[/tex]

=>      [tex]F  =  2500 *  15[/tex]

=>      [tex]F  =  37500 \ \frac{lbm *  ft}{s^2}[/tex]

Now converting to foot-pound-second we have  

         [tex]F =  \frac{37500}{32.2}[/tex]

=>        [tex]F =  1164.6\  lbf[/tex]

Answer:

8v

Explanation:

First we apply super position principle

Vt= v1 + v2+ v3

Remove qa

But vt= 20v

So V = v2+v3

V1= 20-15

= 5v

Remove qb

V= v1+v3

V=8v

So the potential when qa and qc are remove is the potential due to qb

Which is 8v

Answer: Stress can adversely affect sleep quality and duration, while insufficient sleep can increase stress levels. Both stress and a lack of sleep can lead to lasting physical and mental health problems.

Explanation:

Many report that there stress increases when the length and quality of their sleep decreases. When you do not get enough sleep, 21 percent of adults report feeling more stressed.

Answer: 4.speed

Explanation:

In this case, we know that the cart remains at a constant 20km/h.

Now, one could say that "the velocity remains constant, because it always is 20km/h"

But remember that velocity is a vector, so this has a direction, and if the cart is going around a turn, then the direction of motion is changing, which tell us that there is acceleration.

But the module of the velocity, the speed, remains constant at 20km/h.

Then the correct option is 4, speed.