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
(b) Calculate the distance between the first and third islands.
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
distance between the second and third islands = r23 = 8.11 km
distance between the first and third islands = r13 = 7.59 km
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