A truck moves 70m east, then moves 120m west, and finally moves east again a distance of 90 m. If east is chosen as the positive direction, what is the trucks resultant displacement?
The truck ends up 160 miles east and 120 miles north of where it started. Perform a vector addition. It looks like you have a 3-4-5 right triangle, so the answer might be obvious.
To find the truck's resultant displacement, we need to calculate the net distance and direction it has traveled.
First, let's determine the net distance traveled by the truck. We can subtract the distance traveled in the opposite direction from the distance traveled in the positive direction.
Distance traveled east = 70 m
Distance traveled west = 120 m
Distance traveled east (again) = 90 m
Net distance traveled = (70 m + 90 m) - 120 m
= 160 m - 120 m
= 40 m
The net distance traveled by the truck is 40 meters.
Now let's determine the direction of the truck's resultant displacement. Since east is chosen as the positive direction, we consider distances to the east as positive and distances to the west as negative.
The truck initially traveled 70 m to the east (+70 m), then 120 m to the west (-120 m), and finally, 90 m to the east (+90 m).
To find the resultant displacement, we add up the positive and negative displacements:
+70 m + (-120 m) + 90 m = 40 m
Since the resultant displacement (+40 m) is positive, it means the truck ended up 40 meters to the east of its starting position.
Therefore, the truck's resultant displacement is 40 meters to the east.