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?
3 m/s
4 m/s
5 m/s
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.
