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 2m/s
No direction no length of river how broad river is then how to find?
To find out how long it will take the boatman to cross the river, we need to consider the relative motion of the boat and the river.
Let's assume that the river is flowing from west to east. The boatman wants to travel from one side of the river (south bank) to the opposite side (north bank) by taking the shortest path, which is a straight line.
Since the boat is affected by the river's flow, we need to consider the velocity of the boat and the velocity of the river separately.
Given:
- Speed of the boat in still water (independent of any external factors): 3 m/s
- Speed of the river flow: 2 m/s
Now, let's break down the boat's velocity into two components:
1. Velocity of the boat relative to the water: 3 m/s (since the boat can travel at this speed in still water)
2. Velocity of the water: 2 m/s (due to the river's flow)
To find the resulting velocity of the boat, we can use vector addition. Since the boat is crossing the river perpendicular to the flow, we can use the Pythagorean theorem to determine the magnitude of the resulting velocity:
Resulting velocity = √(velocity of the boat relative to the water)^2 + (velocity of the water)^2
= √(3^2 + 2^2) m/s
= √(9 + 4) m/s
= √13 m/s
Now that we have the resulting velocity of the boat, we can calculate the time it will take to cross the river using the formula:
Time = Distance / Velocity
Since the boatman wants to cover the shortest distance, which is a straight line from the south bank to the north bank, the distance can be considered as the width of the river.
Let's assume the width of the river is 'd' meters. Therefore, the time it will take to cross the river is:
Time = d / √13 seconds
So, the boatman will take 'd / √13' seconds to cross the river, where 'd' is the width of the river.