Question

Precalc: Vector word problem:
A channel flows from north to south at a rate of 15 mph.
A sailboat heads at an angle of 30 degrees upstream at 40 mph.
A strong wind blows towards northwest at 30 mph.

a. Write each vector in component form.

Answer 1

bearing in mind that   $\bf \begin{cases} x=rcos(\theta )\\\\ y=rsin(\theta ) \end{cases}$

I can make this much from that, check the picture below.

Answer 2

1. The vector representing the flow from North to South is 0, -15.
2. The vector representing the sailboat is $15\sqrt{3} ,\;15$.
3. The vector representing the strong wind blowing towards northwest is $-15\sqrt{2},\;15\sqrt{2}$ .

What is a vector?

A vector can be defined as an element of a vector space, which represents an object that has both magnitude and direction.

Assuming that; $\left \{ {{x=rcos \theta} \atop {y=rsin \theta}} \right.$

For the channel:

• Rate, r = 15 mph.

The vector representing the flow from North to South is given by:

$15 cos (\frac{3\pi}{2} ), \; 15 sin (\frac{3\pi}{2} )\\\\15(0),\; 15(-1)$

Vector = 0, -15

For the sailboat:

• Rate, r = 40 mph.

• Angle = 30 degrees upstream.

The vector representing the sailboat is given by:

$40 cos (30 ), \; 40 sin (30)\\\\30(\frac{\sqrt{3} }{2} ),\; 30(\frac{1 }{2} )\\\\15\sqrt{3} ,\;15$

Vector = $15\sqrt{3} ,\;15$

For the strong wind:

• Rate, r = 30 mph.

The vector representing the strong wind blowing towards northwest is given by:

$30 cos (\frac{3\pi}{4} ), \; 30 sin (\frac{3\pi}{4} )\\\\30(\frac{-\sqrt{2} }{2} ),\; 30(\frac{\sqrt{2} }{2} )\\\\-15\sqrt{2},\;15\sqrt{2}$

Vector = $-15\sqrt{2},\;15\sqrt{2}$

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