1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Gwar [14]
3 years ago
11

A man starts walking from home and walks 2 miles at 20° north of west, then 4 miles at 10° west of south, then 3 miles at 15° no

rth of east. If he walked straight home,
(a)-how far would he have to walk?

(b)-In what direction would he have to walk?
Physics
1 answer:
Rzqust [24]3 years ago
3 0

Answer:

a)  R = 2.5 mi   b)  To return to your case you must walk in the opposite direction or θ = 98º

This is 8º north west

Explanation:

This is a distance exercise with vectors the best way to work these is to decompose the vectors and perform the sum on each axis separately

To use the Cartesian system all angles must be measured from the positive side of the x-axis or the signs of the components must be assigned manually depending on the quadrant where they are.

First vector A = 2 to 20º north west

Measured from the positive x axis is θ = 180 -20 = 160º

We use trigonometry to find the components

     Cos 20 = Aₓ / A

     sin 20 = A_{y} / A

    Aₓ = A cos 160 = 2 cos 160

    A_{y}  = A sin160 = 2 sin160

    Aₓ = -1,879 mi

    A_{y}  = 0.684 mi

Second vector B = 4 mi 10º west of the south

Angle θ = 270 - 10 = 260º

    cos 2600 = Bₓ / B

    sin 260 = B_{y} / B

    Bₓ = B cos 260

     B_{y}  = B sin 260

    Bₓ = 4 cos 260

     B_{y}  = 4 sin 260

     Bₓ = -0.6946mi

     B_{y}  = - 3,939 mi

Third vector C = 3 mi to 15 north east

     cos 15 = Cₓ / C

     sin15 = C_{y} / C

     Cₓ = C cos 15

     C_{y} = C sin15

     Cₓ = 3 cos 15

    C_{y} = 3 sin 15

     Cₓ = 2,898 mi

    C_{y} = 0.7765 mi

Now we can find the final position of the person

    X = Aₓ + Bₓ + Cₓ

    X = -1.879 -0.6949 + 2.898

    X = 0.3241 mi

    Y = A_{y} +  B_{y} + C_{y}

    Y = 0.684 - 3.939 +0.7765

    Y = -2.4785 mi

a) We use Pythagoras' theorem

     R = √ (x2 + y2)

     R = √ (0.3241 2 + (-2.4785) 2)

     R = 2.4996 mi

     R = 2.5 mi

b) let's use trigonometry

     Tan θ = y / x

     Tanθ  = -2.4785 / 0.3241

     θ = tan⁻¹ (-7,647)

     θ = -82

Measured from the positive side of the x axis is Te = 360 - 82 = 278º

(90-82) south east

To return to your case you must walk in the opposite direction or Te = 98º

This is 8º north west

You might be interested in
A magnifying glass or a hand lens is a bi-convex lens. It is convex on both sides, meaning that the glass is curved outward to
tankabanditka [31]

Answer:

Refracted

Explanation:

If on UsaTestPrep

7 0
3 years ago
When measuring espresso for a drink, which instrument would give the<br> greatest precision?
Gemiola [76]

How many mL is an espresso?

One shot of espresso is generally about 30–50 ml (1–1.75 oz), and contains about 63 mg of caffeine (3). Important point: The “golden ratio” for espresso is this: a single shot is 30 to 44 mL (1 to 1.5 ounces) of water and 7 grams of coffee

5 0
2 years ago
Where in the world is there a Continental Crust with Continental Crust collision?
Savatey [412]

Answer:

c

Explanation:

betweeb the north american and eurasian planes

8 0
2 years ago
Read 2 more answers
Un ciclista recorre 10 km en 2 h.Calcula su velocidad media en km/h.¿cuantos metros recorre cada segundo
lys-0071 [83]

Answer:

La velocidad media es 5 \frac{km}{h}, que equivale a 1.389 \frac{m}{s}

Explanation:

La velocidad es una magnitud física que expresa la relación entre el espacio recorrido por un objeto y el tiempo empleado para ello.

La velocidad media relaciona el cambio de la posición con el tiempo empleado en efectuar dicho cambio. Por lo que se calcula como la distancia recorrida por un objeto dividido por el tiempo transcurrido:

velocidad=\frac{distancia}{tiempo}

En este caso:

  • distancia= 10 km= 10,000 m (siendo 1 km= 1,000 m)
  • tiempo= 2 h= 7,200 s (siendo 1 h= 3,600 s)

Entonces, reemplazando en la definición de velocidad media:

velocidad=\frac{10 km}{2 h}= \frac{10,000 m}{7,200 s}

Resolviendo se obtiene:

velocidad=5 \frac{km}{h}= 1.389\frac{m}{s}

<u><em>La velocidad media es 5 </em></u>\frac{km}{h}<u><em>, que equivale a 1.389 </em></u>\frac{m}{s}<u><em></em></u>

4 0
3 years ago
According to the first law of thermodynamics, the amount of work done by a heat engine equals the amount of
AleksandrR [38]
C. thermal energy added to the engine minus the waste heat.

The law exemplifies conservation of energy. 
<span />
4 0
3 years ago
Read 2 more answers
Other questions:
  • How can working together help scientist achieve their goals?
    5·1 answer
  • What is 52,427 equal in scientific notation
    14·2 answers
  • Electrons do not move unless they are attracted to an electromagnet <br><br> True or false
    11·2 answers
  • [04.05] An atom has an atomic number of 12 and a mass number of 25. How many neutrons does the atom have?​
    9·1 answer
  • When you look ahead while driving, it is best to:
    7·1 answer
  • Why do people eat vegetables? Not just to stay healthy!!! But why else do we eat and need vegetables?
    7·1 answer
  • Define 1 joule work ?​
    12·1 answer
  • A ball starts from rest and rolls down a hill at a constant acceleration of 5 m/s2. If it travels for 8 m how fast is it going i
    9·1 answer
  • If I am lifting a box with a force of 100 N and the box has an acceleration of 10 N, what is the mass of the box?
    14·1 answer
  • How is the way that allows us to listen to an AM/FM Radio in our car is different from the wave that allows us to listen to mu
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!