A boat needs to travel straight across a river. The current is 10 km/hr. The boat can travel at 16 km/hr. What is the velocity of the boat relative to the bank?
If the boat is headed upstream, so that it moves directly across the stream, then
sinTheta=10/16 where theta is the angle upstream frm the line across.
then velocity across= 16cosTheta
a boat can travel 3m/s in still water. a boatman wants to cross a river while covering shortest distance. how long will it take him to cross the river if speed of water is (a) 2m/s (b) 4 m/s
To find the velocity of the boat relative to the bank, we need to consider the effect of the river current.
To start, let's visualize the problem. We have a boat trying to travel straight across a river with a current. Let's assume that the boat is heading directly across the river from one bank to the other. We need to determine the boat's velocity relative to the bank.
First, we need to understand that velocity is a vector quantity, meaning it has both magnitude (speed) and direction. In this case, our boat's velocity relative to the bank has two components: the velocity of the boat in still water and the velocity of the river current.
Here's how we can calculate it:
1. Let's assume the boat's velocity in still water is v_boat = 16 km/hr. This is the speed the boat can maintain in the absence of any external forces.
2. The river current has a velocity of v_current = 10 km/hr. It acts perpendicular to the boat's intended path, considering it flows across the river.
3. Since the boat is trying to move directly across the river, we can use vector addition to determine the resultant velocity relative to the bank. The resultant velocity vector will point from the starting bank of the boat to the ending bank.
4. To find the resultant velocity vector, we use the Pythagorean theorem. The magnitude of the resultant velocity (V_resultant) is given by:
V_resultant = √(v_boat^2 + v_current^2)
Substituting the given values:
V_resultant = √(16^2 + 10^2) = √(256 + 100) = √356 ≈ 18.87 km/hr
So, the velocity of the boat relative to the bank is approximately 18.87 km/hr.