Physics Question

[NNM]

A man entered a cave and walked 100 m north. He then made a sharp turn 150 degrees to the west and walked 87 m straight ahead. Howe far is the man from when he entered the cave? (Note: Sin30=.5, cos 30=.87)

I have tried solving the problem multiple ways, I still get around 180-190 m as my answer, however, the correct answer is 150 m. I have spent at least 2 hours to figure this out, however, nothing. Any answer will be appreciated.

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[Pisiform]

A man went straight North 100m ... then he made a 150 degree turn in counter-clockwise direction which means angle inside the the turn is 180-150 = 30 degrees.... Now he went for another 87m in that direction and stopped. If you now draw a sketch of this and draw a dotted line from the point where he stopped to his originating point. Now draw another dotted line from his end point straight down the 100m line to divide the triangle into 2 triangles such that the dotted line makes 90 degree with each of them. Now find the base of the larger triangle Cos 30 = B / 87 so B = 87 * 0.87 = 75.69. So 100 - 75.69 = 24.31. Now do the same thing for the other side ... Sin30 = P / 87 ... P = 87 * 0.5= 43.5m. Now you can find x by using Pythagoras x = sqrt (24.32)^2 + 43.5^2 = 50m is the final answer

... I still don't understand how the answer could be 150m??

 

[shoehornlettuce]

I got 50m. Using vector addition you have:

-100m north
-87m @ 60 degrees south of west

separate into components:

X
cos(60)*87 = -43.5

Y
100m
sin(60)*87 = -75.3

Sum them up and you have (-43.5, 24.7) from center so distance from center will be 50m.

 

[chiddler]

I got 50m. Using vector addition you have:

-100m north
-87m @ 60 degrees south of west

separate into components:

X
cos(60)*87 = -43.5

Y
100m
sin(60)*87 = -75.3

Sum them up and you have (-43.5, 24.7) from center so distance from center will be 50m.

i like this solution

 

[MedPR]

Nevermind, bad logic. You are probably drawing your vectors wrong, as I did the first time I looked at it. Make the guy turn 90 degrees west, then 60 degrees more, and then draw your 87m vector (it will be drawn southwest). The angle between 87m and 100m is 30.

If you know your cos/sin values, you recognize that cos60 = .87, which = 87/100. So now you know it's a right triangle with 100 as the hypotenuse. Alternatively, depending on the answer choices, you can probably estimate what the length of the unknown vector is just by size (TBR uses dash marks to do this in Physics chapter 1).

 

[MedPR]

87-50-100 is a right triangle. As the others have said, 50 should be the answer.

 

[MedPR]

Nevermind.