Two bicyclists, starting at the same place, are riding toward the same campgroun
ID: 1886013 • Letter: T
Question
Two bicyclists, starting at the same place, are riding toward the same campground by different routes. One cyclist rides 1290 m due east and then turns due north and travels another 1410 m before reaching the campground. The second cyclist starts out by heading due north for 1890 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) In what direction (measured relative to due east within the range (-180, 180]) must the second cyclist head during the last part of the trip?
Explanation / Answer
given
displacement along east x = 1290 m
displacement along north is y = 1890-1410 = 480 m
resultant displacement d = sqrt(x^2+y^2)
d = sqrt(1290^2+480^2) = 1376.4 m
b) direction
theta = tan^-1(y/x) = tan^-1(480/1290) = 20.4 degrees from east