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 cyclist starts out by heading due north for 1870 m and then turns and heads directly toward the campground.

Question

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 cyclist starts out by heading due north for 1870 m and then turns and heads directly toward the campground. 
(a) At the turning point, how far is the second cyclist from the campground? 
(b) What direction (measured relative to due east) must the second cyclist head during the last part of the trip?

drwls · Answer

I will be glad to critique your work. We are getting more physics questions than we can handle in a timely manner, and have to be selective about who receives help.
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Your information on the first cyclist establishes the vector distance of campground from the starting point. Call that vector A. The distance traveled by the second biker on the first leg is vector B.

The answer to your both questions requires calculating the vector difference
A - B.