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Q 25P

Physics For Scientists & Engineers
Found in: Page 73

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Short Answer

Your dog is running around the grass in your back yard. He undergoes successive displacements 3.50m south, 8.20 m northeast, and 15.0 m west. What is the resultant displacement?

|R|=9.48m, θ=166°

See the step by step solution

Step by Step Solution

Step 1: Define magnitude and direction

  • In simple terms, magnitude means 'distance or number.' It depicts the absolute or relative size or direction in which an object moves in the feeling of motion. It's a term for describing the size or scope of something.
  • When we talk about direction, we're talking about a straight-line segment that connects two places in space. The direction is from the beginning (first) to the end (second).

Step 2: Determine the resultant displacement vector

Let us consider the given data.

d1=-3.5mj^d2=8.2×cos 45° mi^+8.2×sin 45° mj^=(5.8i^+5.8j^)md3=-15mi^

We sum the different displacements given in the problem to determine the resultant displacement.


Step 3: Determine the magnitude and direction of the resultant vector

The magnitude and direction of the resultant vector are then determined.

|R|=Rx2+Ry2|R|=(-9.2)2+(2.3)2|R|=9.48 mθ=tan-1RyRx+180°=tan-12.3-9.2+180°=166°

Hence, the resultant displacement is |R|=9.48m, θ=166°

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