A person walks 30 meters due north, then 50 meters at an angle of 35 degrees. Find their total displacement.
Answer (2)
Using the cosine rule (a^2 = b^2 + c^2 - 2bc cos A), we can work out the displacement: Displacement = a b = 30 c = 50 A = 180 - 35 = 145 degrees.
a^2= 900 + 2500 -1500*-0.81915... = 3400 + 1228.728... = 4628.72... a = 68.034... = 68.0m (to 3s.f.).
To work out the angle from starting place, use another configuration of the cosine rule: cos ( C ) = 2 ab a 2 + b 2 − c 2 :
cos (C)= 2 ∗ 68 ∗ 30 4628.72... + 900 − 2500 = 3028.7.../4080 = 0.7423... C = 42.069... degrees = 042 bearing
The total displacement of the person after walking 30 meters north and then 50 meters at an angle of 35 degrees is approximately 76.5 meters. This displacement is directed at an angle of about 68.3 degrees north of east. The calculations involve breaking the walk into north-south and east-west components and using vector addition to find the resultant displacement.
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