A truck travels due east for a distance of 1.1 km, turns around and goes due west for 8.8 km, and finally turns around again and travels 2.8 km due east.
(a) What is the total distance (in km) that the truck travels? (Enter a number.)
km
(b) What are the magnitude (in km) and direction of the truck's displacement? (Enter a number.)
magnitude
km
direction
east
west
neither
To find the total distance that the truck travels, you need to add up the distances traveled in each direction.
(a) Total distance traveled = distance traveled east + distance traveled west + distance traveled east
Distance traveled east = 1.1 km
Distance traveled west = 8.8 km
Distance traveled east = 2.8 km
Total distance traveled = 1.1 km + 8.8 km + 2.8 km
Total distance traveled = 12.7 km
Therefore, the total distance that the truck travels is 12.7 km.
(b) To find the magnitude and direction of the truck's displacement, we need to determine the net distance and direction traveled.
Net distance = distance traveled east - distance traveled west
Distance traveled east = 1.1 km
Distance traveled west = 8.8 km
Net distance = 1.1 km - 8.8 km
Net distance = -7.7 km
The negative sign indicates that the displacement is in the opposite direction of the original direction (east).
The magnitude of the displacement is the absolute value of the net distance, so:
Magnitude of displacement = |net distance|
Magnitude of displacement = |-7.7 km|
Magnitude of displacement = 7.7 km
Therefore, the magnitude of the truck's displacement is 7.7 km to the west.