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In an attempt to escape a desert island, a castaway builds a raft and sets out to sea. The wind shifts a great deal during the d

nikdorinn [45]

Answer:

R = 7,34 km

Ф = 63,43° north of east

Step-by-step explanation:

Let´s analyze each movement and find its perpendicular components. Then, we are going to add the components along the x and y axes to get the resultant and finally to calculate its magnitude and direction.

To determine the perpendicular components, we will use right triangles trigonometrics ratios.

Please see images for each displacement in attached file.

Displacement A: 2.50 km and 45° north of west

Ax= AcosФ = 2.50cos45° = 1.77 km (neg. direction)

Ay= AsenФ = 2.50sen45° = 1.77 km (pos. direction)

Displacement B: 4.70 km and 60° south of east

Bx= BcosФ = 4.70cos60° = 2,35 km (pos. direction)

By= BsenФ = 4.70sen60° = 4,07 km (neg. direction)

Displacement C: 1.30 km and 25° south of west

Cx= CcosФ = 1.30cos25° = 1,18 km (neg. direction)

Cy= CsenФ = 1.30sen25° = 0.55 km (neg. direction)

Displacement D: 5.10 km due east (0°)

Dx= DcosФ = 5.10 km (pos. direction)

Dy= DsenФ = 0 km

Displacement E: 1.70 km and 5° east of north

Ex= EsenФ = 1.70sen5° = 0,15 km (pos. direction)

Ey= EcosФ = 1.70cos5° = 1.69 km (pos. direction)

Displacement F: 7.20 km and 55° south of west

Fx= FcosФ = 7.20cos55° = 4.13 km (neg. direction)

Fy= FsenФ = 7.20sen55° = 5.90 km (neg. direction)

Displacement G: 2.80 km and 10° north of east

Gx= GcosФ = 2.80cos10° = 2.76 km (pos. direction)

Gy= GsenФ = 2.80sen10° = 0.49 km (pos. direction)

Now, we add the components along the x- and y- axis to find the components of the resultant (R):

Rx = Ax + Bx + Cx + Dx + Ex + Fx + Gx

Ry = Ay + By + Cy + Dy + Ey + Fy + Gy

Therefore,

Rx= (-1.77)+(2.35)+(-1.18)+(5.10)+(0.15)+(-4.13)+(2.76)

Ry= (1.77)+(-4.07)+(-0.55)+(0)+(1.69)+(-5.90)+(0.49)

Note: minus (-) symbol to negative directions

Rx = 3.28 km

Ry = - 6.57 km

Let´s use the Theorem of Pythagoras to find the magnitud ot the resultant:

$R = \sqrt{Rx^{2} +Ry^{2} }$

$R =\sqrt{(3.28)^{2}+(-6.57)^{2} }$

R = 7,34 km

To find the direction of the resultant:

tanФ = $\frac{Ry}{Rx}$

tanФ = $\frac{6.57}{3.28}$

tanФ = 2.00

Ф = tan-1 (2.00)

Ф = 63,43° north of east

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3 0

3 years ago

BRAIN TO CORRECT ANSWER!!

Masteriza [31]

Answer:

The final outcome impact of the Civil War was that the North had won the war and slavery was abolished. The impact of the Civil War was the evolution of new war weapons and changes in the economy and the way people lived.The final outcome impact of the Civil War was that the North had won the war and slavery was abolished. The impact of the Civil War was the evolution of new war weapons and changes in the economy and the way people lived.The final outcome impact of the Civil War was that the North had won the war and slavery was abolished. The impact of the Civil War was the evolution of new war weapons and changes in the economy and the way people lived.The final outcome impact of the Civil War was that the North had won the war and slavery was abolished. The impact of the Civil War was the evolution of new war weapons and changes in the economy and the way people lived.The final outcome impact of the Civil War was th\

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Fred has 36 strawberries and 42 blueberries. He wants to use them to garnish desert so that each desert has the same number of b

DENIUS [597]

To do this problem you must find the GCF or the greatest common factor of 36 and 42. For example 36 can be made by 1 and 36 2 and 18 3 and 12 4 and 9 and 6 and 6. 42 can be made by 1 and 42 2 and 21 3 and 14 and 6 and 7. The highest common factor is 6. So, if you put 6 berries on all of the desserts, you will put 6 strawberries on 6 tarts and 6 blueberries on 7 tarts. That’s a total of 13 desserts

7 0

3 years ago

A tire maker produces 20000 tires to be shipped. they inspect 200 of the tires and find that 16 or defective. how many tires of

Xelga [282]

$\frac{16}{200} = \frac{2}{25}$
is the proportion of tires that are defective so
$\frac{2}{25} \times 20000 = 1600$
so we would expect around 1600 tires to be defective

4 0

3 years ago

What is the 10th term in the increasing pattern shown? 1, 1, 2, 3, 5, 8, 13

Vika [28.1K]

Answer:

55

Step-by-step explanation:

(after the first "1") You need to add the previous two numbers together to get the next number in the pattern.

7 0

3 years ago