Question

A ferryboat transports tourists among three islands. It sails from the first island to the second island, 4.29 km away, in a direction 37.0° north of east. It then sails from the second island to the third island in a direction 59.5° west of north. Finally, it returns to the first island, sailing in a direction 28.0° east of south.

(a) Calculate the distance between the second and third islands.


(b) Calculate the distance between the first and third islands.

Answer 1

distance between first and second island = r12 = 4.29 km

displacement vector r12 = r12*cos37 i + r12*sin37 j = 4.29*cos37i + 4.29*sin37 j

distance between second and third island = r23 = ?

displacement vector r23 = -r23*sin59.5 i + r23*cos59.5 j

distance between first and third island = r13 = ?

displacement vector r13 = r13*sin28 i - r13*cos28 j

r12 + r23 + r13 = 0

4.29*cos37i + 4.29*sin37 j -r23*sin59.5 i + r23*cos59.5 j + r13*sin28 i - r13*cos28 j = 0

( 4.29*cos37) - (r23*sin59.5) + (r13*sin28) = 0...........(1)

(4.29*sin37) + (r23*cos59.5) -( r13*cos28) = 0...........(2)

solving 1 and 2

r23 = 8.11 km

r13 = 7.59 km

(a)

distance between the second and third islands = r23 = 8.11 km

(b)

distance between the first and third islands = r13 = 7.59 km