Question

Pre-Lab for LAB#3 Problem 1 3-Put - An example in Vector Addition (or poor golf skills) A golfer, putting on a green requires three strokes to "hole the ball." During the first putt, the ball rolls 5.0 m due east. For the second putt, the ball travels 2.1 m at an angle of 20° north of east. The third putt is 0.50 m due north. What displacement (magnitude and direction relative to due cast) would have been needed to "hole the ball" on the very first putt? Use components to solve this problem. Solution Identify the three vectors. Sketch the vectors and show the vector sum. Include a coordinate system. Identify the components of the three vectors (labeled a, b, c) Determine the components of the resultant vector (labeled s) Convert this into the magnitude and direction of the resultant vector (measured from the positive r axis) Ill - 4 Physics 1200

Answer 1

1. The golfer needs to putt in the 9.9 degree direction to the east to goal in the first putt with displacement of ball with 7.078m.
   htha tho : hs an bu Sn = ant but cn
   
   According to question firstly ball rolls som east and in second putt 21m with 20° angle north of east and in 3rd pult o.som in north dirh So let we take surface as two dimensional Cartesian coordinates with following fig as a direction as east !ct us assume the distance travelled by ball in first putt is a, and in second put is b and so in third put distances travel is c. so the distance travelled by ball in the a direction will be the sum of all the a components. The a component of vector a is an & y component is ay as we know for a vector r a its component is Ru=Rcoso and y component Ry: Rsino where is the angle of vector to the naxis Rsino is Rcoso so. an- acoso = a - 5.0m ay - a sino = 0 similarly for vector bi br - bcos 20° - bx10.9396) - 9.1*0.9396 - 1.9733
   
   Ry by= b singo 24* 0.3420 = 0.7102 and I cn = 0. 5cos 90° cy= o.s sengo So = 0.5 total distance travel by ball in the a dira Sn = ant butan = 5.0+ 1.9733 +0 - 6.973 Total distance travel by ball in the y dirh 5 - 94 + 4* С. - 0 + 0.7182 +0.5 = 1.2182 1 - 6.973 a vector R axis having + 1.2182 ý 1 making o angle with the component Ru . and Ry For and o- tan- (Ry S (6.973) + (1.2102 50.106 m2 - S 1.078 mere
   
   The resultant with a axis. angle of the tano - Ry 6.973 1.918 6.973 = 0.17469 0 = tan (0.1747) 10 9.901 Resultant is 1.010m with g.go to the east