A BOAT WHICH HAS A SPEED IS 5 Km/Hr IN STILL WATER CROSSES A RIVER OF WIDTH 1 Km along the shortest possible path in 15 minutes. find velocity of the river water.
its average speed across is 4km/hr.
draw the diagram.
using the pyth theorem,
5^2=vs^2+4^2
looks like the velocity of the stream is 3Km/hr
Vbw = 1km/15Min = 1km/0.25h = 4km/h =
Velocity of boat with respect to the water.
Vbw = Vb + Vw = 4i
5i + Vw = 4i
Vw = -1i = 1km/h[-90o] = 1km/h Due South
To find the velocity of the river water, we can make use of the concept of relative velocity.
Let's assume the velocity of the river water is v km/hr.
When the boat is crossing the river, it is moving in two different directions simultaneously. One is its own forward motion (speed in still water) and the other is the velocity of the river water, which affects its direction of movement.
The boat travels a distance of 1 km in 15 minutes, which is 1/4 hour. Since speed = distance/time, we can calculate the speed of the boat relative to the shore (the shortest possible path across the river) using the formula:
Speed = Distance / Time
Relative Speed = Speed of Boat - Speed of River Water
1 = (5 - v) / (1/4)
Now, let's solve this equation to find the velocity of the river water:
1 = (5 - v) * 4
1 = 20 - 4v
4v = 20 - 1
4v = 19
v = 19/4
Therefore, the velocity of the river water is 4.75 km/hr.