During a car ride Sandy drives 28.0 km [N] then turns and drives 16.0 km [S 30.˚ E] she makes one final turn and drives an additional 4.00 km [S].  What is her total displacement on this ride?

To find Sandy's total displacement, we need to consider the direction and magnitude of each leg of her journey.

1. Sandy drives 28.0 km north (N). This means her displacement in the north direction is +28.0 km.

2. Sandy then turns and drives 16.0 km south 30° east (S 30° E). To determine her displacement in this direction, we need to break it down into its north and east components. Using trigonometry, we can find that the north component is -14.6 km and the east component is +13.9 km. Therefore, her displacement in this direction is (-14.6 km, +13.9 km).

3. Finally, Sandy drives an additional 4.00 km south (S). This means her displacement in the south direction is -4.00 km.

To find the total displacement, we need to add up the north, east, and south components separately.

North component: +28.0 km East component: +13.9 km South component: -14.6 km - 4.00 km = -18.6 km

Adding these components together, we get: Total displacement = (+28.0 km) + (+13.9 km) + (-18.6 km) = +23.3 km

Therefore, Sandy's total displacement on this ride is 23.3 km.