Question

What is the magnitude of your displacement when you follow directions that tell you to walk 225 m in one direction, make a 90° turn to the left and walk 350 m, then make a 30° turn to the right and walk 125 m?​

Answer 1

Start by facing East. Your first displacement is the vector

d₁ = (225 m) i

Turning 90º to the left makes you face North, and walking 350 m in this direction gives the second displacement,

d₂ = (350 m) j

Turning 30º to the right would have you making an angle of 60º North of East, so that walking 125 m gives the third displacement,

d₃ = (125 m) (cos(60º) i + sin(60º) j )

d₃ ≈ (62.5 m) i + (108.25 m) j

The net displacement is

d = d₁ + d₂ + d₃

d ≈ (287.5 m) i + (458.25 m) j

and its magnitude is

|| d || = √[ (287.5 m)² + (458.25 m)² ] ≈ 540.973 m ≈ 541 m