A truck travels due east for a distance of 1.3 km, turns around and goes due west for 8.9 km, and finally turns around again and travels 3.0 km due east.
(a) What is the total distance that the truck travels?
(b) What are the magnitude and direction of the truck's displacement?
To solve this problem, we need to calculate the total distance traveled by the truck as well as its displacement.
(a) To find the total distance traveled, we simply add up the distances traveled in each leg of the journey.
Distance traveled east = 1.3 km
Distance traveled west = 8.9 km
Distance traveled east again = 3.0 km
Total distance traveled = 1.3 km + 8.9 km + 3.0 km = 13.2 km
So, the truck travels a total distance of 13.2 km.
(b) The displacement of an object gives us information about its change in position. To find the magnitude and direction of the truck's displacement, we need to find its final position relative to its initial position.
When the truck travels east for 1.3 km, its displacement is positive, as it moves in the positive direction on the x-axis.
When the truck travels west for 8.9 km, its displacement is negative, as it moves in the negative direction on the x-axis.
Finally, when the truck travels east again for 3.0 km, its displacement is positive, as it moves in the positive direction on the x-axis.
Now, we can calculate the total displacement:
Total displacement = sum of all positive displacements - sum of all negative displacements
Total displacement = 1.3 km + 3.0 km - 8.9 km = -4.6 km
The negative sign indicates that the displacement is in the opposite direction of the initial motion.
So, the magnitude of the truck's displacement is 4.6 km and its direction is west.
To find the total distance that the truck travels, we add up the distances of each leg of the journey.
(a) Total distance = Distance traveled east + Distance traveled west + Distance traveled east again
= 1.3 km + 8.9 km + 3.0 km
= 13.2 km
Therefore, the total distance that the truck travels is 13.2 km.
To find the magnitude and direction of the truck's displacement, we need to calculate the net displacement. Displacement is a vector quantity that represents the straight-line distance and direction from the starting point to the ending point.
To solve for the displacement, we need to break down each leg of the truck's journey into its x-component (east) and y-component (north). Since the truck is only traveling in the east direction, there is no north component.
(b) Magnitude of displacement = Distance traveled east - Distance traveled west
= 1.3 km - 8.9 km
= -7.6 km (negative sign indicates the direction is west)
Direction of displacement = towards the west
Therefore, the magnitude of the truck's displacement is 7.6 km in the west direction.