Greatest Magnitude of Displacement
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2. Which vector diagram represents the greatest magnitude of displacement for an object ? (A) A path with two segments of $2m$ at a $90^{\circ}$ angle. (B) A path with two segments of $2m$ at a $75^{\circ}$ angle. (C) A path with three segments of $2m$ forming three sides of a rectangle. (D) A path with four segments of $2m$ forming a full rectangle.
This question includes visual content: The image shows four options labeled (A), (B), (C), and (D), each representing a displacement path consisting of segments of length 2m. (A) Two perpendicular segments (90 degrees). (B) Two segments meeting at a 75-degree angle. (C) A path consisting of three segments (vertical up, horizontal right, vertical down). (D) A path consisting of four segments (a closed rectangular loop).
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Step by Step Written Solution
Hi Gnyanesh, let's analyze these vector diagrams to find which one represents the greatest magnitude of displacement.
Displacement Analysis
First, we must remember that displacement is a vector quantity that represents the straight-line distance from the starting position to the final position.
Let's examine Diagram A. The object moves 2 meters up and then 2 meters to the right at a 90-degree angle.
Case (A)
The magnitude of displacement is the length of the hypotenuse of this right triangle. Using the Pythagorean theorem, we find the displacement is approximately 2.83 meters.
Now, let's look at Diagram B. Here, the two 2-meter segments meet at a 75-degree angle.
Case (B)
We can use the Law of Cosines to calculate the distance between the start and end points. This gives us about 2.43 meters.
Because the interior angle is smaller than 90 degrees, the endpoints are closer together than they were in case A.
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