Questions: A boat begins at A and heads straight across a river. Because of the 2 m/s river current, the boat lands on the opposite shore at C. If the river current was 3 m/s, then the boat would land on the opposite shore at (The boat speed relative to the water does not change.) a. the same location of C b. a location south of C c. a location north of C d. Nonsense! This is impossible to answer without knowing the time to cross the river.

A boat begins at A and heads straight across a river. Because of the 2 m/s river current, the boat lands on the opposite shore at C. If the river current was 3 m/s, then the boat would land on the opposite shore at (The boat speed relative to the water does not change.)
a. the same location of C
b. a location south of C
c. a location north of C
d. Nonsense! This is impossible to answer without knowing the time to cross the river.

Transcript text: A boat begins at A and heads straight across a river. Because of the $2 \mathrm{~m} / \mathrm{s}$ river current, the boat lands on the opposite shore at C. If the river current was $3 \mathrm{~m} / \mathrm{s}$, then the boat would land on the opposite shore at $\qquad$ (The boat speed relative to the water does not change.) a. the same location of $C$ b. a location south of $C$ c. a location north of C d. Nonsense! This is impossible to answer without knowing the time to cross the river.

Solution

Solution Steps

Step 1: Analyze the boat's motion

The boat is trying to move directly across the river from point A to point B. However, the river current pushes the boat downstream. The boat's actual velocity is the vector sum of its velocity relative to the water and the water's velocity relative to the shore.

Step 2: Consider the effect of increased current

If the river current increases from 2 m/s to 3 m/s, the boat will be pushed further downstream. Since the boat's velocity relative to the water remains constant, the time it takes to cross the river will also remain constant.

Step 3: Determine the landing point

Since the boat is pushed further downstream with the increased current, it will land at a location south of C.