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MrMuchimi
3 years ago
12

A ship travels 200 miles due west, then adjusts its course 30° north of west. The ship continues on this course for 30 miles. Ap

proximately how far is the ship from where it began?
Mathematics
2 answers:
VARVARA [1.3K]3 years ago
7 0

Answer:

Approximately the ship is 174.67 m far from where it began

Step-by-step explanation:

Let positive x axis represent east and positive y axis represent north.

A ship travels 200 miles due west.

Displacement, s₁ = -200 i

Then adjusts its course 30° north of west. The ship continues on this course for 30 miles.

Displacement, s₂ = 30 cos 30 i + 30 sin 30 j = 25.98 i + 15 j

Total displacement = s₁ + s₂ = -200 i +25.98 i + 15 j = -174.02 i + 15 j

\texttt{Magnitude =}\sqrt{(-174.02)^2+(15)^2}=174.67m

Approximately the ship is 174.67 m far from where it began

Marta_Voda [28]3 years ago
6 0

Answer:

174.66\ mi  or 175\ mi

Step-by-step explanation:

we know that

Applying the law of cosines

c^{2}=a^{2}+b^{2}-2(a)(b)cos(C)

In this problem we have

a=200\ mi

b=30\ mi

C=30\°

substitute the values

c^{2}=200^{2}+30^{2}-2(200)(30)cos(30\°)

c^{2}=30,507.695

c=174.66\ mi

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