A golfer takes three strokes to get the ball into the hole once he is on the green. The first stroke displaces the ball 12 ft. north, the second stroke 6.0 ft. southeast, and the third stroke 3.0 ft. southwest. What displacement was needed to get the ball into the hole on the first stroke?
add them as vectors, but break each up as N,E vectors.
1) 12N
2) 6*cos45 S+6*sin45E= -6cos45 N + 6 sin45 E.
3) 3*cos45 W + 3*sin45 S= -3*cos45E-3sin45N
add them
how do you get 45 degree angel...
To find the displacement needed to get the ball into the hole on the first stroke, we need to calculate the net displacement of the golfer's three strokes.
Let's break down each stroke and convert the distances into a vector form:
1) The first stroke displaces the ball 12 ft. north. We can represent this as a vector (0, 12), where the x-component is 0 (no displacement in the east-west direction) and the y-component is 12 ft. north.
2) The second stroke is 6.0 ft. southeast. This can be represented as a vector (-6.0, -6.0). The negative x-component indicates a displacement in the west direction, and the negative y-component indicates a displacement to the south.
3) The third stroke is 3.0 ft. southwest. This can be represented as a vector (-3.0, -3.0). The negative x-component indicates a displacement in the west direction, and the negative y-component indicates a displacement to the south.
Now, we can add these vectors together to get the net displacement.
Adding the vectors (0, 12), (-6.0, -6.0), and (-3.0, -3.0) gives us (-6.0, 3.0).
To find the displacement needed to get the ball into the hole on the first stroke, we just need to consider the x-component of the net displacement vector. In this case, the x-component is -6.0 ft (displacement in the west direction).
Therefore, the displacement needed to get the ball into the hole on the first stroke is 6.0 ft west.