One day you go hiking at a nearby nature preserve. At first, you follow the straight, clearly marked trails. From your starting point, y?
It helps to draw this so you can keep track of how you are moving in the original coordinate system. So, draw it with me as we do this. Get a piece of paper and a pencil. 1) Draw the original coordinate system. The problem does not give a direction for the trails, so to make it easy, we will assume that Trail 1 is straight up the y axis Trail 1: 2.0 mi in the + Y direction to (0, 2.0) Trail 2: Turn 30 deg CCW and go 1.6 mi (2nd quadrant, x is negative and y is positive.) cos 30 = y/1.6 y = 1.6 * 0.87 = 1.39 mi in the + y direction ===> y = +1.39 mi sin 30 = x/1.6 x = 0.5 * 1.6 = 0.8 mi in the - x direction ===> x = - 0.8 mi So, our position at the end of trail 2 is ((0 - 0.8), (2.0 + 1.39) = (- 0.8, 3.39) Trail 3: Turn 160 CW, but we already turned 30 CCW, so the net turn in the original coordinate system is 160 - 30 = 130 degrees. So, in the original coordinate system, turn 130 degrees CW from the y axis that puts us 130 - 90 = 40 degrees below the x axis in the 4th quadrant ( x is positive and y is negative) and go 2.2 mi cos 40 = x/2.2 x = 0.77 * 2.2 = 1.69 mi ====> + 1.69 mi sin 40 = y/2.2 y = 0.64 * 2.2 = 1.41 ===> - 1.41 mi So, our position at the end of trail 3 is: (( - 0.8 + 1.69), (+3.39 - 1.41)) = ( 0.89, 1.98) Distance back to camp R^2 = 0.89^2 + 1.98^2 R^2 = 0.79 + 3.92 = 4.71 R = 2.17 mi angle to turn CW (right) tan^-1 = 0.89/1.98 = 0.45 angle = 24.2 deg
One day you go hiking at a nearby nature preserve. At first, you follow the straight, clearly marked trails. From your starting point, you?
Keep track of position as you move along. Let's say the first path points in the direction of the +x-axis. End of first path: Ax = 2.00 mi End of second path: Ax = 2.00 + 1.60cos30.0° mi Ax = 3.386 mi Ay = 1.60sin30.0° mi Ay = 0.80 mi End of third path: Ax = 3.386 + 2.20cos(30.0° - 160°) mi Ax = 1.972 mi Ay = 0.80 + 2.20sin(30.0° - 160°) mi Ay = -0.885 mi Reference angle to to help you get back to where you started: tanθ = Ay / Ax tanθ = (-0.885) / (1.972) θ = -24.1° (24.1° clockwise from +x-axis) But we need to go the other direction: 180 - 24.1° = +155.9° And you're facing 30.0° - 160° = -130° (or 360° - 130° = +230°) at the end of the third path, so you'll need to turn 230° - 155.9° = 74.1° to the right And walk a distance: A = sqrt[(Ax)² + (Ay)²] A = sqrt[(1.972 mi)² + (-0.885 mi)²] A = 2.16 mi
How is Nagalapuram trekking?
Nagalapuram a beautiful place which became ugly because of molesters,eve teasers.We had visited this place this May 1st 2017. The place is dry this time. Some small natural pools are still visible. The more you trek in the forest the more it portrays it's lacquer. We did not reach to the final magic pool because a lot of eve teasers. They had started bothering us. On the way back two of them molested one of us after blocking our way where the forest is secluded and we hit them for our defence and had to run. The molesters again followed us to take revenge on us because we had hit them. This time we had found two people to whom we approached for help. But without helping us they ran for their life. We had fought against one molester. Another molester had already parted this one and disappeared into the forest. This time one of us tried to click a photo of the molester when he hit one of us on head and was continuously hitting until another of us hit him to save the other. Then the molester slit the hand of one of us but this time the molester became powerless as we had also hit him for our defence. Then we collected the wounded, blooded ourselves and ran for our life. We had not crossed the half of the way to reach the main trekking parking, again we saw the molester running towards us but he was way behind us. Finally as we reached almost 1km towards the main trekking parking some eve-teasers started bothering us. This time we ignored them and reach the main parking. As we were bleeding we had taken help from the couple who do maintain the trekking parking. But this time we did not tell them any molester was following us because last time when we asked for help from two other persons they did not help us. We had told them we fall down so we were bleeding. They had done some very basic first aid. We asked them if we can get an auto to nagalapuram village and they helped us to reach nagalapuram village. And finally we reached our home wounded but alive.
Physics Question- 2 Dimensional Kinematics?
One day you go hiking at a nearby nature preserve. At first, you follow the straight, clearly marked trails. From your starting point, you travel 2.00 miles down the 1st trail. Then you turn to your left by 30.0° to follow a 2nd trail for 1.50 miles. Next, you turn to your right by 160° and follow a 3rd trail for 1.80 miles. At this point you are getting very tired and would like to get back as quickly as possible, but all of the available trails seem to lead you deeper into the woods. You would like to take a shortcut directly through the woods (ignoring the trails). How far to your right should you turn, and how far do you have to walk, to go directly back to your starting point? I know that the distance is 2.2324 miles, but I can not get the angle correct. I do know that 50, 116, 65, 73, and 106 degrees are all wrong. Thanks for your help!