Multiple choice

A boat is moving with the velocity of $4 \hat{i}+ 4\hat{j}$ relative to the stream. The speed of the stream is $ - \hat{i}$. What is the displacement of the boat in $10 \ seconds$? (Enter numerical value only)

  1. $40$
  2. $30$
  3. $50$
  4. $20$
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C Correct answer
Explanation

Velocity of boat relative to ground = (4i + 4j) + (-i) = 3i + 4j. Speed = sqrt(3^2 + 4^2) = 5. Displacement in 10 seconds = 5 * 10 = 50.

AI explanation

To find the actual velocity, add the boat's velocity relative to the stream (4i + 4j) to the stream's velocity (-1i), resulting in an actual velocity of 3i + 4j. The magnitude of this velocity is sqrt(3^2 + 4^2) = 5 units per second. Multiplying this speed by the time of 10 seconds gives a displacement of 50.

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