Suppose you take two steps A and B (that is, two nonzero displacements). Under what circumstances can you end up at your starting point? More generally, under what circumstances can two nonzero vectors add to give zero? Is the maximum distance you can end up from the starting point A+B the sum of the lengths of the two steps?
Two non-zero displacements can be zero only if they have equal magnitude but are headed in the opposite directions. Yes, the maximum distance we can end up from the starting point is the sum of the lengths of the two steps.
A distance is the actual path covered by a moving object. It is a scalar quantity that cannot be zero or negative.
A displacement is the shortest path covered by a moving body from an initial position to reach a final position. It is a vector quantity, which can be zero or negative under certain conditions.
Two non-zero vectors add up to zero only if their magnitude is equal, but they are headed in the opposite directions.
Hence, if we take one step along the north and another step of the same length along the south, we will end up at the starting point.
A distance is a scalar quantity, which can be added according to simple algebraic rules.
If you take one step of length A and another step of length B, then the maximum distance traveled is:
Hence, the maximum distance one can end up from the starting point is the sum of the lengths of the two steps.
In an attempt to escape his island, Gilligan builds a raft and sets to sea. The wind shifts a great deal during the day, and he is blown along the following straight lines: north of west; then south of east; then south of west; then straight east; then east of north; then south of west; and finally north of east. What is his final position relative to the island?
An owl is carrying a mouse to the chicks in its nest. Its position at that
time is 4.00 m west and 12.0 m above the center of the 30.0 cm diameter nest. The owl is flying east at 3.50 m/s at an angle 30.0º below the horizontal when it accidentally drops the mouse. Is the owl lucky enough to have the mouse hit the nest? To answer this question, calculate the horizontal position of the mouse when it has fallen 12.0 m.
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