Question

You are riding in a boat whose speed relative to the water is 5.0 m/s. The boat points at an angle of 25.8° upstream on a river flowing at 14.8 m/s. Find the time it takes for the boat to reach the opposite shore if the river is 26.5 m wide.

Answer 1

@Abhisar can you help with this one?

Answer 2

Is this an accurate drawing of what you're talking about?

Answer 3

those are both accurate

Answer 4

Actually only one is right. I'm not sure if the angle is measured from the horizontal like @Abhisar 's picture or the vertical like mine.

Answer 5

i think @walking_stick is more accurate but if you look at @Abhisar and see the opposite shore as the far right it could be seen as accurate

Answer 6

"The boat points at an angle of 25.8° upstream "

Answer 7

upstream means the flow of river in opp direction of boat's motion.

Answer 8

okay, but what equation do I use?

Answer 9

okay, so would we use the 90 angle the 26.5m side and the 25.8 angle?

Answer 10

Scratch that, we can use the cosine trig function.

\[\cos(\theta)=adjacent/hypotenuse\]

Answer 11

We know theta and the length of the adjacent side. We are solving for the hypotenuse

Answer 12

so the cos(25.8)=26.5/h?

Answer 13

Correct. You can use a calculator to solve cos(25.8).

Answer 14

cos(25.8)= .7855

Answer 15

Okay. Then we can use algebra to solve for h.

Answer 16

so would it be...33.736? multiply both sides by h then divide by .7855

Answer 17

so now I have to find how long it takes

Answer 18

How you said you solved it is right, but that's not the number I get for \[26.5/\cos(25.8)\]

Answer 19

i still get the same answer. 26.5/(cos(25.8))

Answer 20

is 33.736

Answer 21

cos(25.8)=0.9003187714

Is your calculator set to degree mode?

Answer 22

ohhh. sorry i'm on my sister's calculator. yes you're correct

Answer 23

http://www.wolframalpha.com/input/?i=cos%2825.8+degrees%29

Answer 24

i changed it now

Answer 25

Okay :). Now we're cooking. So what's your new distance?

Answer 26

so there answer is 29.434

Answer 27

please tell me that's right

Answer 28

That's what I get.

Answer 29

We know that speed equals distance over time.

Answer 30

what gets me is how you would calculate the speed of the boat against the current of the stream

Answer 31

Ah yes, I forgot about the current.... Let me think for a moment.

Answer 32

Ah, yes. It's another trig problem. Here's a picture.... (in a second as I draw it lol)

Answer 33

so...pythagorean theorem?

Answer 34

We use the same angle, but now we are using a different trig function. Which one does it look like we should use?

Answer 35

Or yes, the pythagorean theorem.

Answer 36

haha much easier that way

Answer 37

which means \[5^{2}+14.8^{2}=244.04\]
and \[\sqrt{244.04}=15.622\]

Answer 38

so that would be the new speed, 15.622m/s?

Answer 39

Exactly... and nice use of the equation tool.