Two bicyclists, starting at the same place, are riding toward the same campgroun
ID: 1951245 • Letter: T
Question
Two bicyclists, starting at the same place, are riding toward the same campground by two different routes. One cyclist rides 1370 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 1930 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?
Explanation / Answer
Choose the starting point as origin, +x = east, +y = north
From the first one, we know his displacement is 1470 i + 1430 j
then for the second one, 1940 j + A = 1470 i + 1430 j
so vector A = 1470 i - (1940 - 1430) j = 1470 i - 510 j
a) |A| = 1556 m
b) tan-1(510/1470) = 19.1o (south of east)