Vectors Problem Packet Homework Solutions (18-23)

In conclusion, the cake will travel South 51.5o West. 18. Two ants at a picnic find a small piece of cake. Each picks up the cake and tries to carry it home. The first ant’s home is at a bearing of [W 15o N] and he pulls with a force of 10 dynes. The second ant’s home is at a bearing of [S 15o W] , and he pulls with a force of 13.5 dynes. What do you predict will happen? In which direction will the cake travel? x-components: 10 dynes 15o -9.66 + (-3.49) = -13.15 dynes 2.59 y-components: 9.66 15o 2.59 + (-13.04) = -10.45 dynes In conclusion, the cake will travel South 51.5o West. 13.5 dynes 13.04 16.8 dynes 51.5o 10.45 3.49 13.15

19. Linda is pulling a sled with a force of 20 pounds and is heading on a bearing of N30E. Elaine begins to pull the sled with a force of 15 pounds on a bearing of N5W. What force is exerted on the sled and in which direction does it go? 32.26 8.69 1.31 10 17.32 14.94 15 lbs 20 lbs 5o 33.4 lbs 15.1o 30o x-components: -1.31 + 10 = 8.69 lbs y-components: 14.94 + 17.32 = 32.26 lbs

+ = 20. Find the resultant of a 120-Newton force North and an 80 Newton force at N45 E. 56.57 120 N + = 185 N 56.57 45o 80 N 176.57 x-components: 0 + 56.57 = 56.57 N 72o 56.57 y-components: 120 + 56.57 = 176.57 N

21. Two water skiers are being pulled by a boat 21. Two water skiers are being pulled by a boat. The first skier exerts a force of 300 pounds North on the boat; the second skier exerts a force of 400 pounds at N75 E. Find the resultant of the two forces. 386.37 = 300 lbs + 103.53 75o 386.37 400 lbs 403.53 558.7 lbs 43.8o x-components: 0 + 386.37 = 386.37 lbs y-components: 300 + 103.53 = 403.53

22. Three brothers are playing at the local playground with a frisbee 22. Three brothers are playing at the local playground with a frisbee. Each grabs it at the same time. Robbie grabs it at the N63 E point and exerts a force of 100 pounds on it. Chip grabs it at the N27 W point and exerts a force of 100 pounds on it. Ernie pulls with 141.4 pounds at the S18 W point. Who gets control of the frisbee? 45.399 100 lbs 141.4 lbs 89.101 89.101 27o 63o 18o 45.399 x-components: -45.399 + 89.101 + (-43.399) = 0 y-components: 89.101 + 45.399 + (-134.479) = 0 134.479 Since both sets of components are zero, NOBODY wins (the frisbee doesn’t even move) 43.695

x-components: 10 dynes 15o -9.66 + (-3.49) = -13.15 dynes 2.59 y-components: 9.66 15o 2.59 + (-13.04) = -10.45 dynes To balance the piece of cake, the 3rd ant would have to cancel out the resultant of the other two ants. 13.5 dynes 13.04 16.8 dynes 51.5o 10.45 3.49 13.15 16.8 dynes [N 51.5o E]