P..D #8 - PHYS240 - SPRING 2018 NAME: Assignment: Read Text-Chapter 3 and Chapte

Question

P..D #8 - PHYS240 - SPRING 2018 NAME: Assignment: Read Text-Chapter 3 and Chapter 4, plus complete Weekly Engagement Activity POD8-PROBLEM 1. Position vectors A golfer takes three putts to get the ball into the 18th hole. The first putt displaces the ball 3.66 m north of the hole, the second putt displaces the ball 1.83 m southeast of the hole and the third moves the ball 0.91m southwest of the hole. What are a) the magnitude b) the direction of the displacement required to get the ball into the hole in one putt from its first position? Hint: draw a detailed figure to figure out the starting point and the position of the hole.

Explanation / Answer

Let , east is x direction and north is y direction

measuring all angles from east, anti-clockwise is +ve , clockwise is -ve

split into x and y components in the form of vectors

a = 3.66 m north = (0 , 3.66)

b = 1.83 m southeast = (1.83cos(-45) , 1.83sin(-45))

c = 0.91 m southwest = (0.91cos(-135) , 0.91sin(-135))

now add a,b and c

a+b+c = (0 , 3.66) + (1.83cos(-45) , 1.83sin(-45)) + (0.91cos(-135) , 0.91sin(-135))

= (1.83cos(-45)+0.91cos(-135) , 3.66 + 1.83sin(-45) + 0.91sin(-135) ) ~ ( 0.651 , 1.72 )

a) || ( 0.651 , 1.72 ) || = sqrt (0.651^2 + 1.72^2 ) ~ 1.84m by Pythagorus theorem

b) tan(theta) = 1.72/0.651

so, theta = arctan(1.72/0.651) ~ 69.3°

so the hole is 1.84m at 69.3° north of east

Please rate my answer, good luck...

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