Answer:
(a) The truck travels a total distance of 15.1 kilometers.
(b) The magnitude of the truck's displacement is 4.5 kilometers, and the direction is west.
Step-by-step explanation:
Let's break down the truck's journey step by step:
The truck travels due east for 2.0 km.
The truck turns around and goes due west for 9.8 km.
The truck turns around again and travels 3.3 km due east.
(a) To find the total distance the truck travels, you simply add up the distances covered in each step:
Total distance = 2.0 km + 9.8 km + 3.3 km = 15.1 km
So, the truck travels a total distance of 15.1 kilometers.
(b) The magnitude of the truck's displacement can be found using the Pythagorean theorem, as displacement is the straight-line distance between the initial and final positions.
The truck traveled east for 2.0 km and then traveled west for 9.8 km, which results in a net displacement to the west of 9.8 km - 2.0 km = 7.8 km.
The truck then travels east again for 3.3 km. The net displacement from the starting point will be the difference between the westward displacement and the eastward displacement:
Net displacement = 7.8 km - 3.3 km = 4.5 km
The direction of the displacement will be the direction of the final position from the initial position. Since the net displacement is to the west, the direction is west.
So, the magnitude of the truck's displacement is 4.5 kilometers, and the direction is west.