Question

a person in a boat wishes to cross a river from point o to point 2, as shown in the figure. the water has velocity $v_{water}=5\\ m/s$ in the positive $x$-direction relative to the river bank, and the boat has a velocity of $v_{boat}=10\\ m/s$ in the positive $y$-direction relative to the water. towards which point should the boat travel to reach point 2 and why?
toward point 1 because the $y$-component of the boat’s velocity with respect to the water needs to be equal in magnitude to the velocity of the water.
toward point 1 because the $x$-component of the boat’s velocity with respect to the water needs to be equal in magnitude to the velocity of the water but in the opposite direction.
toward point 2 because the magnitude of the boat’s velocity with respect to the water is greater than the magnitude of the velocity of the water.
toward point 2 because the $y$-component of the boat’s velocity with respect to the water is not affected by the motion of the water.
answer c
incorrect. this answer indicates that the velocity of the water has no effect on the resultant velocity of the boat as the boat

Explanation:

To reach Point 2, the boat needs to counter - act the water's flow in the x - direction. The water is flowing in the positive x - direction with velocity \(v_{water}=5\ m/s\). So, the boat must have an x - component of velocity relative to the water that is equal in magnitude and opposite in direction to the water's velocity. This will cancel out the effect of the water's flow in the x - direction and allow the boat to move directly towards Point 2.

Answer:

B. Toward Point 1 because the x - component of the boat’s velocity with respect to the water needs to be equal in magnitude to the velocity of the water but in the opposite direction.