Notes Ask Your Teach are 3.90 m to the north, 2.20 m northeast, and 0.90 m at 25

Question

Notes Ask Your Teach are 3.90 m to the north, 2.20 m northeast, and 0.90 m at 25 0" west of south. Starting at the same initial point, an A novice golfer on the green takes expert golfer could make the hole in what single displacement? three okes to sink the bal The successive d gla em ts (north of east) My Ask Your Teachs Instructions for finding a buried treasure incude the foowing Go 80 0 paces at 225, turn to 120P and w walk 105 paces, then travel 100 paces at 1579 The angles are measured to the east, the dction Determine the resant placement from the starting point

Explanation / Answer

1) let East be +x axis

x-component of resultant displacement,
Rx = 2.20*cos(45) - 0.9*sin(25)

= 1.175 m

y-component of resultant displacement,
Ry = 3.90 + 2.20*sin(45) - 0.9*cos(25)

= 4.64 m

resultant displacement, R = sqrt(Rx^2 + Ry^2)

= sqrt(1.175^2 + 4.64^2)

= 4.79 m <-----Answer

direction : theta = tan^-1(Ry/Rx)

= tan^-1(4.64/1.175)

= 75.8 degrees <-----Answer

2)

Rx = 80*cos(225) + 105*cos(120) + 100*cos(157)

= -201.1 paces

Ry = 80*sin(225) + 105*sin(120) + 100*sin(157)

= 73.4 paces

so, |R| = sqrt(Rx^2 + Ry^2)

= sqrt(201.1^2 + 73.4^2)

= 214 paces

direction : theta = tan^-1(Ry/Rx)

= tan^-1(73.4/201.1)

= 20.0 + 180

= 200 degrees  

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