To analyze the movement of the object from point A to point D based on the given points, let's break down the distances correctly.
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Points A, B, C, and D:
- A(0, 0)
- B(3, 30)
- C(6, 30)
- D(11, 0)
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Distance Calculations:
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From A to B: The distance can be calculated using the distance formula:
\[ \text{Distance (A to B)} = \sqrt{(3-0)^2 + (30-0)^2} = \sqrt{3^2 + 30^2} = \sqrt{9 + 900} = \sqrt{909} \approx 30.15 , m \] -
From B to C:
Since B and C are horizontally aligned (same y-coordinate), the distance can be calculated as: \[ \text{Distance (B to C)} = C_x - B_x = 6 - 3 = 3 , m \] -
From C to D:
Similar to above, since C and D are also diagonally positioned, we have: \[ \text{Distance (C to D)} = \sqrt{(11-6)^2 + (0-30)^2} = \sqrt{5^2 + (-30)^2} = \sqrt{25 + 900} = \sqrt{925} \approx 30.41 , m \] -
From A to D: Lastly, the distance from A to D: \[ \text{Distance (A to D)} = \sqrt{(11-0)^2 + (0-0)^2} = \sqrt{11^2} = 11 , m \]
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Evaluating the Options:
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(a) In the interval from point C to point D, the object travels 0 m.
- False (the distance is \(\approx 30.41\) m).
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(b) In the interval from point A to point D, the object travels 11 m.
- True (correct as per our calculations).
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(c) In the interval from point A to point B, the object travels 30 m.
- False (it travels approximately 30.15 m).
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(d) In the interval from point B to point C, the object travels 30 m.
- False (the distance is 3 m).
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Based on all the calculations, the only true statement is:
b. In the interval from point A to point D, the object travels 11 m.
1 answer