Two beetles run across flat sand, starting at the same point. Beetle 1 runs 0.50

Question

Two beetles run across flat sand, starting at the same point. Beetle 1 runs 0.50 m due east, then 0.82 m at 25 degree north of due east. Beetle 2 also makes two runs and the first is 1.6 m at 44 degree east of due north. What must be the magnitude of its second run if it is to end up at the new location of beetle 1? In what direction must it run? Find the vector sum of the two beetle-1 runs. Write the first betle-2 run as vector. You want the difference between those two vectors (that is, the magnitude and direction from beetle 2 to the final point of beetle 1).

Explanation / Answer

a) For beetle 1 = 0.50 i + (0.82cos25 i + 0.82sin25 j)

                         = (1.243 i + 0.3465 j) m

     For beetle 2 = (1.6cos46 i + 1.6sin46 j)

                           = (1.11 i + 1.151 j) m

=>    second run =    (1.243 i + 0.3465 j) -   (1.11 i + 1.151 j)

                             = (0.133 i - 0.8045 j) m

=> magnitude of second run = 0.8154 m

b)    Direction =   360 - tan-1(0.8045/0.133)

                       = 279.38 degree

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