Question

A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are d1 = 4.10 m to the north, d2 = 2.10 m northeast, and d3 = 0.90 m at θ = 30.0° west of south (figure below). Starting at the same initial point, an expert golfer could make the hole in what single displacement?
m
° (north of east)

Answer 1

d_1=(0,4.1)m
d_2=(2.1 cos⁡45,2.1 sin⁡45 )m
d_3=(-0.9 sin⁡30,-0.9 cos⁡30 )m
d=(0+2.1 cos⁡45-0.9 sin⁡30,4.1+2.1 sin⁡45-0.9 cos⁡30 )=(1.035,4.806)m
d=√((1.035)^2+(4.806)^2 )=4.92 m.
θ=tan^(-1)⁡〖4.806/1.035〗=77.9°
Answer: 4.92 m 77.9 ° (north of east)