boat sailing through a river moved eastward for 5 km, then cross the river by moving 3 km southward. On reaching the other side it moved westward through 1 km and reached the dock. Find the displacement covered by the boat in km.
Question
boat sailing through a river moved eastward for 5 km, then cross the river by moving 3 km southward. On reaching the other side it moved westward through 1 km and reached the dock. Find the displacement covered by the boat in km.
Solution
To find the displacement covered by the boat, we need to calculate the net distance and direction from the starting point to the dock.
Step 1: The boat moved eastward for 5 km. This means the boat's position shifted 5 km to the east.
Step 2: The boat then crossed the river by moving 3 km southward. This means the boat's position shifted 3 km to the south.
Step 3: On reaching the other side, the boat moved westward through 1 km. This means the boat's position shifted 1 km to the west.
Step 4: Finally, the boat reached the dock.
To calculate the displacement, we need to find the net distance and direction from the starting point to the dock. We can do this by adding the eastward and westward distances and subtracting the southward distance.
Net distance = (5 km westward) + (1 km eastward) = 4 km westward Southward distance = 3 km
Displacement = √((Net distance)^2 + (Southward distance)^2) Displacement = √((4 km)^2 + (3 km)^2) Displacement = √(16 km^2 + 9 km^2) Displacement = √(25 km^2) Displacement = 5 km
Therefore, the displacement covered by the boat is 5 km.
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