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A boat travels across a river with a speed of 8 km/h relative to the water. If t

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Question: A boat travels across a river with a speed of 8 km/h relative to the water. If the river flows at 6 km/h, what is the speed of the boat relative to the riverbank?

Options:

  1. 8 km/h
  2. 10 km/h
  3. 14 km/h
  4. 6 km/h

Correct Answer: 10 km/h

Solution: 

Speed of boat relative to riverbank = √(8^2 + 6^2) = √(64 + 36) = √100 = 10 km/h.

A boat travels across a river with a speed of 8 km/h relative to the water. If t

Practice Questions

Q1
A boat travels across a river with a speed of 8 km/h relative to the water. If the river flows at 6 km/h, what is the speed of the boat relative to the riverbank?
  1. 8 km/h
  2. 10 km/h
  3. 14 km/h
  4. 6 km/h

Questions & Step-by-Step Solutions

A boat travels across a river with a speed of 8 km/h relative to the water. If the river flows at 6 km/h, what is the speed of the boat relative to the riverbank?
Correct Answer: 10 km/h
  • Step 1: Identify the speed of the boat relative to the water, which is 8 km/h.
  • Step 2: Identify the speed of the river current, which is 6 km/h.
  • Step 3: Understand that the boat's speed and the river's speed form a right triangle, where the boat's speed is one side and the river's speed is the other side.
  • Step 4: Use the Pythagorean theorem to find the resultant speed of the boat relative to the riverbank. The formula is: Speed = √(boat speed² + river speed²).
  • Step 5: Substitute the values into the formula: Speed = √(8² + 6²).
  • Step 6: Calculate 8², which is 64.
  • Step 7: Calculate 6², which is 36.
  • Step 8: Add the two results: 64 + 36 = 100.
  • Step 9: Take the square root of 100, which is 10.
  • Step 10: Conclude that the speed of the boat relative to the riverbank is 10 km/h.
  • Relative Velocity – Understanding how to calculate the resultant speed of an object moving in a medium that is also in motion.
  • Pythagorean Theorem – Applying the theorem to find the resultant speed when two velocities are perpendicular to each other.
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