A golf ball is to be hit 300 yards straight to make a hole in one. Having only played miniature golf, your first swing makes the ball skew 50 yards N 30 W. Trying to get back on track, the second shot goes 80 yards N 35 E. Now you are very upset with this game and you swing with anger causing the ball to go 200 yards N 10 W. At this point you realize that brut strength is not working and you decide to resort to math. What should be the components of your next swing to finally make in the hole?

changing them to direction vectors with standard angle notation.

50 yards N30°W = 50(cos120,sin120) = (-25,43.30)
80 yards N35E = 80(cos55,sin55) = (45.89 , 65.53
200 yds N10W = 200(cos100,sin100) = (-34.73 , 196.96)
r yds at Ø = r(cosØ,sinØ) = (rcosØ,rsinØ)

adding these we should get (0,300)
rcosØ = (13.84 , -5.79)
r = √(13.84^2 + (-5.79)^2) = 15.00
tanØ = -5.79/13.84
Ø = -22.7° --> in quad IV , looking at (13.84,-5.79)

His shot should be 15 yds at E 22.7° S

I guess it is to be 300 NORTH ? (0,300)

swing 1 x = -25, y = 43.3
swing 2 x = -25+80sin35 y = 43.3+80 cos 35
so now
x = 29.9 y =109
swing 3 x =29.9-200sin10 y = 109+200cos10
so now
x = -4.83 y = 306 getting close

we must go 2.83 east and -6 south

To determine the components of your next swing to make it into the hole, we need to break down the total displacement you need into its north and west components. Let's analyze the given information to calculate these components:

1. Start point: You initially hit the ball 50 yards N 30 W. This means the ball went 50 yards north and 30 yards west.

2. Second shot: The ball went 80 yards N 35 E. This means the ball went 80 yards north and 35 yards east. Since eastward is the opposite direction of westward, the effect of this shot was to cancel out some of the westward displacement from the first shot.

3. Third shot: You hit the ball 200 yards N 10 W. This means the ball went 200 yards north and 10 yards west.

Now, let's calculate the total north and west displacement:

North displacement = (50 yards + 80 yards + 200 yards) = 330 yards north
West displacement = (30 yards - 35 yards - 10 yards) = -15 yards west

To make it into the hole, you need to hit the ball with an opposite displacement in the north and west direction. Therefore, you should swing your next shot with the following components:

North component: -330 yards (to cancel out the previous north displacement)
West component: 15 yards (to cancel out the previous west displacement)

By hitting the ball with these components, you should be able to get back on track and make it into the hole.