Chapter 01, Problem 45 Consult Multiple Concept Example 9 in preparation for thi

Question

Chapter 01, Problem 45 Consult Multiple Concept Example 9 in preparation for this problem. A golfer, putting on a green, requires three strokes to "hole the ball." During the first putt, the ball rolls 2.2 m due east. For the second putt, the ball travels 3.2 m at an angle of 21.0° north of east. The third putt is 0.64 m due north. What displacement ((a) magnitude and (b) direction relative to due east) would have been needed to "hole the ball" on the very first putt? (a) Number Units (b) Number Units

Explanation / Answer

displacement in x-direction,

Rx = 2.2 + 3.2*cos(21) + 0

= 5.19 m

displacement in y-direction,

Ry = 0 + 3.2*sin(21) + 0.64

= 1.79 m

a) magnitude of displacemnt, R = sqrt(Rx^2 + Ry^2)

= sqrt(5.19^2 + 1.79^2)

= 5.49 m

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

= tan^-1(1.79/5.19)

= 19.0 degrees north of east

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