A whale swims due east for a distance of 7.5 km, turns around and goes due west for 2.5 km, and finally turns around again and heads 2.6 km due east.
(a) What is the total distance traveled by the whale?
(b) What are the magnitude and direction of the displacement of the whale?
(a) 7.5 + 2.5 + 2.6
(b) 7.5 - 2.5 + 2.6 (east)
To find the total distance traveled by the whale, we need to sum up the distances traveled in each leg of the journey.
(a) The whale travels 7.5 km due east, then 2.5 km due west, and finally 2.6 km due east. To find the total distance, we add these three distances:
Total distance = 7.5 km + 2.5 km + 2.6 km = 12.6 km.
Therefore, the total distance traveled by the whale is 12.6 km.
(b) To find the magnitude and direction of the displacement, we need to consider the net change in position from the start point to the end point.
The whale starts by swimming 7.5 km due east, then swims 2.5 km back west, and finally swims 2.6 km further east. To find the net change, we subtract the westward movement from the sum of the eastward movements:
Net change = (7.5 km + 2.6 km) - 2.5 km = 7.6 km.
The magnitude of the displacement is the absolute value of the net change, which is 7.6 km.
The direction of the displacement is determined by the final position relative to the starting point. Since the whale moved eastward for a total of 7.5 km + 2.6 km = 10.1 km, and westward for 2.5 km, the whale ends up positioned 7.6 km further east than the starting point. Therefore, the direction of the displacement is due east.
To find the total distance traveled by the whale, we need to add up the distances traveled in each direction.
(a) Total distance traveled by the whale = distance traveled east + distance traveled west + distance traveled east again
Total distance traveled by the whale = 7.5 km + 2.5 km + 2.6 km = 12.6 km
Therefore, the total distance traveled by the whale is 12.6 km.
To find the magnitude and direction of the displacement of the whale, we need to calculate the net displacement. Displacement is a vector quantity, so we need to consider both the magnitude and direction.
(b) Displacement of the whale = net distance traveled in one direction
Net distance traveled in one direction = distance traveled east - distance traveled west
Net distance traveled in one direction = 7.5 km - 2.5 km = 5.0 km
Therefore, the magnitude of the displacement of the whale is 5.0 km.
The direction of the displacement is in the eastward direction, as the whale started and ended its journey by swimming east.
So, the magnitude and direction of the displacement of the whale is 5.0 km east.