Vector Component Words Problem,

[thaolieu]

Vector Component Words Problem, please help :(

A golfer lines up for her first putt at a hole that is 13.5 exactly northwest of her ball’s location. She hits the ball 13.5 and straight, but at the wrong angle, 40 degree from due north.

a)In order for the golfer to have a “two putt green,” determine the angle of the second putt.
Angle= ? degree in south of west

b)Determine the magnitude of the second putt's displacement.

 

[lewando]

Welcome, thaolieu, to PF. The idea here is that if you show some effort at working out the problem then help can be provided. So I must ask you, what have you tried? Can you draw a picture of the situation? What are you confused about, etc.

 

[thaolieu]

I drew the graph that indicate the direction of the ball and putt #1.
Direction of the ball = -13.5x +0y
Putt 1 = 13.5 cos (40)x + 13.5sin (40)y = -3.16x + 8.67y

That's what I got. I hope to receive help to go further. Thank you so much

 

[lewando]

...but at the wrong angle, 40 degree from due north

This is a little ambiguous, let's agree that the golfer is a pretty good putter so this direction is really 40 degrees WEST of NORTH.

I drew the graph that indicate the direction of the ball and putt #1.

To start, your graph should contain 2 vectors: the location of the hole and the location of the ball after the first putt. Can you post your graph, with all the information, to make sure you are starting out correctly?

Direction of the ball = -13.5x +0y

This is a location vector pointing WEST. Please recheck what you are trying to do here. Convention: +x = EAST, +y = NORTH

Putt 1 = 13.5 cos (40)x + 13.5sin (40)y = -3.16x + 8.67y

When you graph -3.16x + 8.67y, does it look right? Specifically, does the angle look like 40 degrees, or not? Does the magnitude = 13.5, or not?

 

[rwisz]

a) To have a "two putt green," the golfer's second putt needs to be aimed in the opposite direction of the first putt, which was at a 40 degree angle from due north. This means the angle of the second putt should be 40 degrees south of west.

b) The magnitude of the second putt's displacement can be calculated using trigonometry. The first putt had a magnitude of 13.5, and the angle of the second putt is 40 degrees. Using the cosine function, we can calculate the magnitude of the second putt's displacement as 13.5*cos(40) = 10.3. Therefore, the golfer's second putt needs to have a magnitude of 10.3 in order to reach the hole in two putts.