Question

Five four wheelers engage in a relay event where the first four wheeler departs at 12 mph at an angle of 20 degrees. it proceeds for 30 minutes reaching four wheeler 2 which proceeds at 9 mph at an angle of 30 degrees for 20 minutes when it reaches the third four wheeler. Four wheeler 3 proceeds at 8 mph for 45 minutes at 0 degrees reaching the 4th four wheeler. The 4th four wheeler drives off at an angle of -40 degrees at a speed of 4 mph for 15 minutes, reaching the last (fifth) four wheeler. The fifth four wheeler must return to the starting point. At what angle and speed must the fifth four wheeler proceed if it is to reach the starting point in 1 hour 20 minutes: (Angles are measured from due east.)

Answer 1

We can treat each distance distance traveled by the four wheelers are vectors. Their sum must be zero since the last four wheeler truck ends up where the first four wheeler truck started
d1∠1 + d2∠2 + d3∠3 + d4∠4 + d5∠5 = 0
d5∠5 = - (d1∠1 + d2∠2 + d3∠3 + d4∠4)
Since we don't know the speed of the fifth wheeler, we just add the angles and equate it to 360
20 + 30 + 0 + -40 + ∠5 = 360
∠5 = 350 or -10
The fifth wheeler must travel at an angle of -10 degrees.