Question

what are the magnitude and direction of the given vector?

A boat would like to cross a river using the most direct route. Because of the current, must aim up river. To the nearest degree, what is the angle the boat should head upstream?

Answer 1

The magnitude of the vector is given from Pythagorean Theorem. It's direction is given from tan(theta) = (6)/(20)

Answer 2

How do you bring tan over to the right side? It becomes (theta)=tan^-1(6/20)

Answer 3

What does the Pythagorean Theorem say?

Answer 4

a^2+b^2=c^2

Answer 5

Good. So what is C ?

Answer 6

20.9

Answer 7

how do you determine direction?

Answer 8

is it north of west?

Answer 9

Yes , but you need an angle to describe that. So it's given from tan(theta)= (opposite/adjacent)= (6/20) . Then just punch into your calculator tan^-1(6/20) and it will give you the angle from west going north.

Answer 10

oh okay! thank you :)

Answer 11

for the second question would it be 19?

Answer 12

Use Pythagorean Theorem to find the missing side, then you can use the genera formula x=tan(theta)= (opposite side/ adjacent side) . Don't skip steps or you're just guessing the answer.

Answer 13

i got 16.9 but thats not one of my choices. i have 19 or 71 as a choice.

Answer 14

16.9 is the side length. So you want the angle the boat needs to be at to counteract the current. So tan(theta)=(6/16.9) which implies theta = 19.54

Answer 15

I should also mention that the angle is in degrees. So the answer would be 19.54 degrees , and to counteract the stream (i.e. head north) the boat needs to face 19.54 degrees north of east.

Answer 16

oh okay.. thank you so much!!!!