Relative Velocity in Two-Dimensional Motion 3rd Six Weeks Exam

Explain how the velocity of a boat is affected by the current of a river.

• It remains constant regardless of the current

• It decreases as the current increases

• It is altered by the river current, affecting the resultant velocity

• It increases with the river current

If a boat travels across a river with a current, how do you determine the resultant velocity of the boat?

• By subtracting the river's velocity from the boat's velocity

• By adding the boat's velocity to the river's velocity

• By vector addition of the boat's velocity relative to the water and the river's current velocity

• By dividing the boat's velocity by the river's velocity

A boat is heading directly across a river with a velocity of 5 m/s relative to the water. The river flows at 3 m/s. What is the magnitude of the boat's resultant velocity?

• 8 m/s

• 2 m/s

• 5 m/s

• 4 m/s

Describe the steps to calculate the time it takes for a boat to cross a river when given the width of the river and the boat's velocity relative to the water.

• Divide the width by the river's velocity

• Multiply the width by the boat's velocity

• Divide the width by the boat's velocity relative to the water

• Add the width to the boat's velocity

A river is 200 m wide and flows at 2 m/s. A boat travels at 4 m/s relative to the water. How long does it take for the boat to reach the opposite bank?

• 50 seconds

• 100 seconds

• 25 seconds

• 200 seconds

A boat needs to reach a point directly across a 100 m wide river. The river flows at 1.5 m/s, and the boat's speed relative to the water is 3 m/s. At what angle should the boat be steered relative to the current to reach the opposite point directly?

• 30 degrees

• 45 degrees

• 60 degrees

• 90 degrees

What is the angle θ when sin θ = 1.5/3?

• 30°

• 45°

• 60°

• 90°

What happens when the river's current speed increases?

• The time to cross the river generally increases.

• The time to cross the river decreases.

• The boat's speed increases.

• The boat's speed decreases.

How should the boat be steered to minimize crossing time?

• In a direction that maximizes its velocity component perpendicular to the current.

• Directly across the river.

• Against the current.

• With the current.

What is the approximate value of √34?

• 5.83

• 6.00

• 5.50

• 5.00