a man wishes to cross a river in a boat .if he crosses the river in minimum time then he takes 10min with a drift of 120 m .if he crosses the river taking shortest route,he takes 12.5min find the velocity of the boat with respect to water.
To find the velocity of the boat with respect to the water, we can set up a system of equations based on the given information.
Let's assume the velocity of the boat in still water is "v" and the velocity of the river current is "u".
1. The time it takes to cross the river with a drift of 120 m is 10 minutes. Since the boat is drifting downstream due to the river current, we need to consider the effective velocity of the boat.
- Effective velocity = v + u (boat's velocity + river current velocity)
- Distance = 120 meters
- Time = 10 minutes = 10 * 60 seconds
So, the equation for the first scenario is: Distance = Effective velocity * Time
- 120 = (v + u) * 600
2. The time it takes to cross the river using the shortest route is 12.5 minutes.
- Effective velocity = v - u (boat's velocity - river current velocity)
- Distance = shortest route distance (unknown)
- Time = 12.5 minutes = 12.5 * 60 seconds
Let's denote the shortest route distance as "d".
So, the equation for the second scenario is: Distance = Effective velocity * Time
- d = (v - u) * 750
Now we have two equations with two unknowns (v and u). We can solve these equations simultaneously to find the values.
Using the first equation: 120 = (v + u) * 600
- Divide both sides by 600: (v + u) = 0.2v + 0.2u
Using the second equation: d = (v - u) * 750
- Divide both sides by 750: (v - u) = 0.00133d
Now, we can equate the expressions for (v + u) using the first equation and (v - u) using the second equation:
0.2v + 0.2u = 0.00133d
Since the value of d is unknown, we cannot find the exact values of v and u. However, we can solve this equation for the ratio of v to u.
Rearranging the equation, we get: v/u = 0.00133d / 0.2 - 0.2
Simplifying further, we get: v/u = 0.00665d - 1
Therefore, we cannot determine the exact velocity of the boat or the current without knowing the shortest route distance ("d").