What Is the Expert Golfer's Ideal Single Stroke on the Green?

[niyati]

A novice golfer on the green takes three strokes to sink the ball. The successive displacements are 4.00 m to the north, 2.00 m northeast, and 1.00 m at 30.0 degrees west of south. Starting at the same initial point, an expert golfer could make the hole in what single displacement?

I drew the picture, but am I to assume northeast means a 45 degree angle? The resultant vector is the sum of all three of these vectors. The first vector, broken down to its components, is 0i + 4j, or [0,4]. The second vector (if I'm assuming it has an angle of 45 degrees) has components of 2.00cos45 and 2.00 sin45, which makes 2/[sq.rt.]2 for both the x and y coordinates. And the third vector must be at an angle of 240 degrees, if it is just 30 degrees off of south in a western direction. Therefore, it is -120 or 240 degrees: h.c. = 1.00cos240 and v.c. = 1.00sin240. If these are all correct, I am just suppose to add each component to its respective component in order to get the resultant components of the expert golfer's shot, right?

 

[learningphysics]

Yes, looks right to me. I agree, northeast seems to imply 45 degrees.

 

[m2003]

I can confirm that your understanding of vector addition is correct. To find the resultant displacement of the expert golfer's shot, we simply add the x and y components of each individual displacement. In this case, the x component would be 0 + 2/[sq.rt.]2 + 1.00cos240 and the y component would be 4 + 2/[sq.rt.]2 + 1.00sin240. Using basic trigonometry, we can simplify these components to get the final displacement of the expert golfer's shot. It is important to note that in reality, the expert golfer's shot may vary slightly due to factors such as wind and terrain, but this calculation provides a good estimate.