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A boat travels across a river with a speed of 4 m/s relative to the water. If th

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Question: A boat travels across a river with a speed of 4 m/s relative to the water. If the river flows at 3 m/s, what is the resultant speed of the boat relative to the riverbank?

Options:

  1. 3 m/s
  2. 4 m/s
  3. 5 m/s
  4. 7 m/s

Correct Answer: 5 m/s

Solution: 

Resultant speed = √(4^2 + 3^2) = √(16 + 9) = √25 = 5 m/s.

A boat travels across a river with a speed of 4 m/s relative to the water. If th

Practice Questions

Q1
A boat travels across a river with a speed of 4 m/s relative to the water. If the river flows at 3 m/s, what is the resultant speed of the boat relative to the riverbank?
  1. 3 m/s
  2. 4 m/s
  3. 5 m/s
  4. 7 m/s

Questions & Step-by-Step Solutions

A boat travels across a river with a speed of 4 m/s relative to the water. If the river flows at 3 m/s, what is the resultant speed of the boat relative to the riverbank?
Correct Answer: 5 m/s
  • Step 1: Identify the speed of the boat relative to the water, which is 4 m/s.
  • Step 2: Identify the speed of the river current, which is 3 m/s.
  • Step 3: Recognize 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. The formula is Resultant speed = √(boat speed^2 + river speed^2).
  • Step 5: Substitute the values into the formula: Resultant speed = √(4^2 + 3^2).
  • Step 6: Calculate 4^2, which is 16, and 3^2, which is 9.
  • Step 7: Add the two results together: 16 + 9 = 25.
  • Step 8: Take the square root of 25, which is 5.
  • Step 9: Conclude that the resultant speed of the boat relative to the riverbank is 5 m/s.
  • Relative Velocity – Understanding how to calculate the resultant speed of an object moving in a medium with a current.
  • Pythagorean Theorem – Applying the theorem to find the resultant speed when two velocities are perpendicular.
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