In What Direction Relative to North Must Canoeist 2 Paddle to Reach the Island?

wr1015

Vectors problem assistance, please!!!

Two canoeists first paddling at the same fourth dimension and head toward a small island in a lake. Canoeist 1 paddles with a speed of 1.60 m/due south at an angle of 45° due north of east. Canoeist two starts on the reverse shore of the lake, a distance d = i.59 km eastward of canoeist 1.

(a) In what direction relative to north must canoeist 2 paddle to reach the island?? the respond in degrees west of north.
(b) What speed must canoeist 2 have if the two canoes are to arrive at the island at the same fourth dimension?

LeonhardEuler

If I empathise the problem correctly, in that location is not enough information. The island could exist anywhere in the lake forth the line canoeist i travels. The direction canoeist 2 travels will depend on exactly where the isle is.

wr1015

If I empathize the trouble correctly, there is not enough information. The island could exist anywhere in the lake along the line canoeist 1 travels. The direction canoeist ii travels will depend on exactly where the isle is.

yeah you are quite right, attached is a picture of the problem above

LeonhardEuler

Await at canoeist 1's path. There is a 45-45-90 triangle consisting of his path, the x-axis, and the perpendicular from the island. Given i of the sides, yous can at present discover the other ii. At present expect at canoeist 2's triangle. Since y'all know the toal distance along the 10-centrality is one.59km, and y'all know one role of it from the 45-45-90 triangle, y'all can subtract to become the short leg of canoeist two's triangle. The angle [itex]\theta[/itex] is congruent to the angle in canoeist 2'southward triangle betwixt the canoeist's path and the long leg, so yous know that [itex]\tan{\theta}=\frac{opp}{adj}[/itex]. Solve for [itex]\theta[/itex]

wr1015

Look at canoeist 1'southward path. At that place is a 45-45-ninety triangle consisting of his path, the x-axis, and the perpendicular from the isle. Given one of the sides, you can at present notice the other 2.
first i would just like to thank you for actually helping me I greatly appreciate it but for some reason I don't recollect I fully understand your response considering I'm assuming you mean that i use pythagorean'due south theorem for this but how would that piece of work?? because that would exist: (1.59km)squared + unknown side squared = hypotenuse (or the path of canoeist one) squared.

LeonhardEuler

first i would just like to thank y'all for actually helping me I greatly appreciate it but for some reason I don't retrieve I fully understand your response considering I'k assuming you mean that i employ pythagorean's theorem for this merely how would that work?? because that would be: (ane.59km)squared + unknown side squared = hypotenuse (or the path of canoeist 1) squared.

Information technology'due south not the pythagorean theorem you're using. A 45-45-90 triangle is an isocelese triangle. This means that the two legs are of equal length. I am looking at the triangle that has information technology's sides as: one-the canoeist 1'south path, 2-the side labled 1km, three-the bottom. The fact that the two legs are equal means that the length of the bottom side is also 1km. The total altitude forth the lesser betwixt the canoers is 1.59km, so the remaining length must be .59. From in that location, do what I said before to get the bending. Also, once you accept that bottom part for canoeist 1'south triangle, you tin can use the pythagorean theorem to discover canoeist 1'due south path length.

wr1015

It's not the pythagorean theorem you're using. A 45-45-90 triangle is an isocelese triangle. This means that the two legs are of equal length. I am looking at the triangle that has it'southward sides as: i-the canoeist ane's path, ii-the side labled 1km, 3-the bottom. The fact that the two legs are equal means that the length of the bottom side is too 1km. The full distance along the bottom between the canoers is ane.59km, so the remaining length must be .59. From there, practise what I said before to get the angle. Also, once you have that bottom role for canoeist 1's triangle, yous can use the pythagorean theorem to discover canoeist i's path length.

thanks very much, that helped me profoundly

Dugdale Ferseelle

In What Direction Relative to North Must Canoeist 2 Paddle to Reach the Island?

Vectors problem aid, please

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