Velocity of the boat with respect to river is 10 m/s. It passes the river and reaches opposite shore at point C. If the velocity of the river is 3m/s, find the time of the trip and distance between B and C

To solve this problem, we need to analyze the motion of the boat and the river's current. The boat has a velocity of 10 m/s relative to the water, and the river flows at 3 m/s. We can break this down into two components: the velocity of the boat across the river and the velocity of the river downstream. Let's go through the steps to find the time of the trip and the distance between points B and C.

Understanding the Motion

The boat is moving across the river, while the river is also moving downstream. We can visualize this scenario as follows:

• Let the width of the river be w.
• The boat's velocity across the river is V_boat = 10 m/s.
• The river's velocity is V_river = 3 m/s.

Calculating Time to Cross the River

To find the time it takes for the boat to reach the opposite shore (point C), we need to know the width of the river. However, since the width is not provided, we can express the time in terms of the width w:

The time t taken to cross the river can be calculated using the formula:

t = w / V_boat

Finding the Distance Downstream

While the boat is crossing the river, it is also being carried downstream by the current. The distance d that the river carries the boat downstream during the time t can be calculated using the river's velocity:

d = V_river * t

Combining the Equations

Substituting the expression for time t into the distance equation gives us:

d = V_river * (w / V_boat)

Now, substituting the known values:

d = 3 m/s * (w / 10 m/s)

d = 0.3w

Final Results

To summarize, the time taken to cross the river is:

t = w / 10

And the distance between points B and C, where the boat lands downstream, is:

d = 0.3w

To find specific numerical values, we would need the width of the river. However, this framework allows you to calculate both the time of the trip and the downstream distance once you have that measurement. If you have the width of the river, you can plug it into these equations to get your final answers!