Physics
posted by RE .
Two bicyclists, starting at the same place, are riding toward the same campground by two different routes. One cyclist rides 1490 m due east and then turns due north and travels another 1430 m before reaching the campground. The second cyclist starts out by heading due north for 2130 m and then turns and heads directly toward the campground.
(a) At the turning point, how far is the second cyclist from the campground?
(blank) m
(b) What direction (measured relative to due east) must the second cyclist head during the last part of the trip?
(blank)° (blank = either north or south) of east

Resolve the displacements into East (x) and North (y) components.
First find the coordinates of the campground relative to the starting point:
Distance angle xcomponent ycomponent
1490 0° 1490cos(0) 1490sin(0)
1430 90° 1430cos(90) 1430sin(90)
Total  1490 1430
Therefore the campground is at (1490,1430) relative to the starting point.
At the turning point, the second cyclist is at (0,2130) relative to the starting point.
The distance from the campground is therefore the distance between the two points (0,2130) and (1490,1430).
The direction of P2(x2,y2) from P1(x1,y1) is atan2(y2y1, x2x1), taking into account of the signs of the values and therefore the quadrant.
In the case in point, the angle is
atan2(14302130,14900) = 25 degrees approximately, or 25 degrees south of east.
Respond to this Question
Similar Questions

physics
Two bicyclists, starting at the same place, are riding toward the same campground by two different routes. One cyclist rides 1100 m due east and then turns due north and travels another 1430 m before reaching the campground. The second … 
physics
Two bicyclists, starting at the same place, are riding toward the same campground by two different routes. One cyclist rides 1500 m due east and then turns due north and travels another 1430 m before reaching the campground. The second … 
physics
Two bicyclists, starting at the same place, are riding toward the same campground by two different routes. One cyclist rides 1500 m due east and then turns due north and travels another 1430 m before reaching the campground. The second … 
PHYSICSHELP!!
Two bicyclists, starting at the same place, are riding toward the same campground by two different routes. One cyclist rides 1500 m due east and then turns due north and travels another 1430 m before reaching the campground. The second … 
physics
Two bicyclists, starting at the same place, are riding toward the same campground by different routes. One cyclist rides 1040 m due east and then turns due north and travels another 1540 m before reaching the campground. The second … 
physics
Two bicyclists, starting at the same place, are riding toward the same campground by different routes. One cyclist rides 1120 m due east and then turns due north and travels another 1550 m before reaching the campground. The second … 
physics
Two beetles run across flat sand, starting at the same point. Beetle 1 runs 0.42 m due east, then 0.72 m at 32o north of due east. Beetle 2 also makes two runs; the first is 1.48 m at 47o east of due north. What must be the magnitude … 
Physics
Two bicyclists, starting at the same place, are riding toward the same campground by different routes. One cyclist rides 1030 m due east and then turns due north and travels another 1480 m before reaching the campground. The second … 
Geometry 1
Ship A and Ship B leave from the same point in the ocean. Ship A travels 150 mi due west, turns 65° toward north, and then travels another 100 mi. Ship B travels 150 mi due east, turns 70° toward south, and then travels another 100 … 
Math( Please Help, Assignment Due)
Isaac stands on the shoreline of a lake and looks to a campground across the lake. He uses a compass to determine that the campground is 60 degrees west of north. He then paddles his canoe north for a distance of 550m. He stops and …