Adhira loves to ride her bike around the neighborhood. She starts riding 1.2 miles at 30° S of E. Then, she rides another 2.0 miles at 20° W of S. Next, she rides 1.6 miles at 30° S of W. And finally, she rides 2.6 miles at 15° W of N. What is her final displacement from her starting point?

Answers

Answer 1

Answer:

D = 1.8677 miles , θ = 24.28º at South of West

Explanation:

This is an exercise in adding vectors, the easiest way to solve them is to decompose the vectors and add each component algebraically. Let's use trigonometry

first displacement. d = 1.2 miles to 30º south of East

     cos ( 360-30) = cos (-30) = x₁ / d

     sin (-30) = y₁ / d

     x₁ = d cos (-30)

     y₁ = d sin (-30)

     x₁ = 1.2 cos (-30) = 1,039 miles

     y₁ = 1.2 sin (-30) = -0.6 miles

second shift. d = 2.0 miles to 20º West of South

       cos (270-20) = x₂ / d

       cos (250) = y₂ / d

       x₂ = 2.0 cos 250 = -0.684 miles

       y₂ = 2.0 sin250 = -1.879 miles

Third displacement. d = 1.6 miles to 30º South of West

       cos (180 + 30) = x₃ / d

       sin (210) = y₃ / d

       x₃ = 1.6 cos 210 = -1.3856 miles

       y₃ = 1.6 sin 210 = -0.8 miles

Fourth displacement. d = 2.6 miles to 15º West of North

       cos (90 + 15) = x₄ / d

       sin (105) = y₄ / d

       x₄ = 2.6 cos 105 = -0.6729 miles

       y₄ = 2.6 sin 105 = 2,511 miles

having all the components we add

x-axis  (West-East direction)

       X = x₁ + x₂ + x₃ + x₄

       X = 1.039 -0.684 - 1.3846 - 0.6729

       X = -1.7025 miles

   

       Y = y₁ + y₂ + y₃ + y₄

       Y = -0.6 -1.879 -0.8 +2.511

       Y = -0.768

The modulus of this displacement is we use the Pythagorean theorem

      D = √ (X² + Y²)

      D = √ (1.7025² + 0.768²)

      D = 1.8677 miles

let's use trigonometry to find the direction

       tan θ = Y / X

       θ = tan⁻¹ Y / x

       θ = tan⁻¹ (0.768 / 1.7025)

       θ = 24.28º

as the two components are negative this angle is in the third quadrant

therefore in cardinal direction form is

         θ = 24.28º at South of West


Related Questions


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Answers

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If someone have weight that is force due to gravity is X than on the sun it will become 28 X.

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A student is given an investigation of the human body. The student is to predict how new cells are created. According to cell theory, which prediction is correct?

A.Cells grow and develop, but are never replaced.

B. New cells are created from pre-existing cells in the human body.

C. New cells are created but quickly die during cell growth.

D. Humans are born with all the cells they will ever need.

Answers

Answer:

B. New cells are created from pre-existing cells in the human body.

Explanation:

According to the cell theory, the correct assumption from the student's investigation is that "new cells are created from pre-existing cells in the human body".

One of the postulates of the cell theory is that all cells originated from pre-existing cells. Also, a cell is the fundamental unit of life.

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Answers

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A. carbon and boron
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Answers

Answer:

A. carbon and boron

Explanation:

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An allow forms between metals and metals using their huge electron could.

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Answer:

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Explanation:

carbon and boron

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Answers

Answer:

[tex]4ms^{-2}[/tex]

Explanation:

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a = [tex]\frac{F}{m}[/tex]

Substitute 20 for F and 5 for m:

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Question 2 (2 points)
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Answer:

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Answers

Answer:

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Explanation:

Answer:

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Explanation:

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Explanation:

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Answer:

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Answer: An independent variable is the variable which is changed. Experiments are usually published to communicate findings to the scientific community.

Disproving a hypothesis means it cannot be tested again.

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Answers

Answer:

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Explanation:

Answer:

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Explanation:

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Answers

Answer:

1. The subduction zone serves as the meeting point for two tectonic plates.

2. At the Mid- Ocean ridge, decompression melting occurs.

3 What causes the magma to rise is the increase in pressure caused by collection of gases by the magma.

Explanation:

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Answer:

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Answers

Answer:

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Explanation:

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Answers

Answer:

because nono gravity

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Answers

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Answers

Answer:

Examples of Newton's third law of motion are ubiquitous in everyday life. For example, when you jump, your legs apply a force to the ground, and the ground applies and equal and opposite reaction force that propels you into the air. Engineers apply Newton's third law when designing rockets and other projectile devices.

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Answers

Answer:

A. The balls stick and move together.

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Answers

Answer:

40.1m/s

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This is a kinematics problem

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Using kinematics equation:

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vf^2 = 0 + 2*(-9.8)*(82)

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Answers

Answer:8 m/s ^2

Explanation:

A car increases velocity from 30 m/s to 60 m/s in 4 seconds. Calculate the average acceleration of the car over this time.
0.3 m/s2
7.5 m/s2
0.6 m/s2
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Answers

Answer:

B.7.5m/s2

Explanation:

average acceleration=change invelocity/time taken

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The average acceleration of the car 7.5 m/s²

The parameters given in the question are;

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time= 4 seconds

The formula that can be used to calculate the average acceleration is

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A student lists a set of materials
1. Wood
2.hydrogen gas
3. Milk
4. Water
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A. hydrogen gas
B.wood
C. Milk and water
D. wood, hydrogen gas, milk, and water

Answers

Answer:

D. wood, hydrogen gas, milk, and water

Explanation:

Waves will transmit through wood, hydrogen gas, milk and water.

Waves are disturbances that propagates energy usually through a material medium.

Most mechanical waves pass through the given medium. Only electromagnetic waves do not really require a material medium for their propagation. They can be propagated through a vacuum.

Write an equation of the line in slope-intercept form.

Answers

the answer would be y=1/3x+2

A net force of 10.N accelerates an object at 5.0 m/s^2. What net force would be required to accelerate the same object at 1.0 m/s^2?
A.) 1.0 N
B.) 5.0 N
C.) 50. N
D.) 2.0 N

Answers

Answer:

I believe the answer is 2.0

Explanation:

The net force that would be required is 2 N

From the question,

We have that

A net force of 10 N accelerates an object at 5.0 m/s².

To determine the net force that would be required to accelerate the same object at 1.0 m/s²,

First, we will determine the mass of the object

From the Newton's second law of motion, we have that

F = ma

Where F is the force

m is mass

and a is acceleration

From the given information

F = 10N

a = 5.0 m/s²

Putting the above parameters into the formula, we get'

10 = m × 5.0

∴ m = 10 ÷ 5.0

m = 2 kg

∴ The mass of the object is 2kg

Now,

For the net force that would be required to accelerate the same object at 1.0 m/s²,

Using the same formula

F= ma

Here,

a = 1.0 m/s²

and m = 2 kg

∴ F = 2 × 1

F = 2 N

Hence, the net force that would be required is 2 N

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A turtle is moving at a speed of 1.5 m/s for a time of 120 s. What is the distance the turtle travels?

Answers

Answer:

The answer is 180 m

Explanation:

The distance covered by an object given it's velocity and time taken can be found by using the formula

distance = velocity × time

From the question we have

distance = 1.5 × 120

We have the final answer as

180 m

Hope this helps you

Answer:

180 meters

Explanation:

1.5 m/s x 120 s

Rate at which wave travels or propagates

Answers

Answer:

v =fλ v = f λ where v

Explanation:

In lab you submerge 100 g of iron nails at 40 0C in 100 g of water at 20 0 C. Specific heat of iron is 0.12 cal/g∙0C. Equate the heat gained by water to the heat lost by nails and show that the final temperature of water becomes 22.1 0C.

Answers

Let T be the final temperature of water and nails (iron).

Given that the initial temperature of 100 g nails, [tex]T_{1F}=40^{\circ}C[/tex].

Specific heat of the iron, [tex]C_F=0.12 cal/g^{\circ}C[/tex].

So, the heat lost by nails [tex]= mC_F(T_{1F}-T}[/tex]

[tex]=100\times 0.12 \times (40-T)\cdots(i)[/tex]

The initial temperature of 100 g water, [tex]T_{1w}=20^{\circ}C.[/tex]

Specific heat of water, [tex]C_w=1 cal/g^{\circ}C[/tex]

So, the heat gained by water [tex]= mC_w(T-T_{1w}}[/tex]

[tex]=100\times 1 \times (T-20)\cdots(ii)[/tex]

As the exergy is conserved, so

the heat lost by the nails = the heat gained by the water

From equation (i) and (ii), we have

[tex]100\times 0.12 \times (40-T)=100(T-20)[/tex]

[tex]\Rightarrow 0.12(40-T)=T-20[/tex]

[tex]\Rightarrow 0.12\times 40 -120T=T-20[/tex]

[tex]\Rightarrow 0.12T+T=4.8+20[/tex]

[tex]\Rightarrow 1.12T=24.8[/tex]

[tex]\Rightarrow T=24.8/1.12= 22.1^{\circ}C[/tex]

Hence, the final temperature of both, iron nails as well as water, become [tex]22.1^{\circ}C[/tex].

the person is not able to see the far lying object clearly. which type of lens will the doctor prescribe him give reason?

Answers

Answer:

correction of farsightedness uses a converging lenses that compensates for the under convergence by the eye. the converging lens produces an image farther from the eye than the object so that farsighted can see it clearly.

how is force spread over long and short durations of time?

Answers

I think you're having trouble with it only because of how you're trying to look at it.

Don't try to imagine "spreading force" over time. Just think about how long the force lasts !

Like . . .

If you push your doll stroller for 5 seconds, you'll get it up to a certain speed.

Next time, if you push it again with the same force, but you keep pushing for TEN seconds, you'll get it up to a faster speed.

Technically:

(force • time) = impulse.

You gave it more impulse the second time, so it got more momentum from you.

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