Question

Please include all steps clearly and draw the diagram too.

Thanks!

Problem 2: Three archeologists on a game show are brought to the centre of a large, flat field. Each is given a meter stick, a compass, a calculator and a shovel, and (in a different order for each contestant) the following 3 displacements: 72.4 m, 32.0° east of northh 57.3 m, 36.0° south of west 17.8 m straight south The 3 displacements lead to the point where dinosaur fossils are buried. Two archeologists start measuring immediately, but the winner first calculates where to go. What does she calculate?

Answer 1

As shown in figure a^rightarrow = 72.4 times [sin 32 degree i^cap + cos 32 j^cap] = 38.37 i^cap + 61.4 j^cap] m b^rightarrow = 57.3 times [-cos (36.0 degree) i^cap - sin (36.0 degree) j^cap] = 57.3 times [-0.8090 i^cap - 0.5878 j^cap] = [-46.36 i^cap - 33.68 j^cap] m c^rightarrow = -17.8 j^cap so a^rightarrow + b^rightarrow + c^rightarrow = (38.37 - 46.36) i^cap + (61.4 - 33.68 - 17.8)j^cap so magnitude resultant displacement = [(7.99)62 + (9.92)^2]^1/2 = 12.7 m and tan theta = -9.92/7.99 = -1.2416 OR theta = (51.15)^0 north as west net displacement = 12.7 m at 51.15 degree north as west