A swimmer wishes to swim across a river 600m wide. If he can swim at the rate of 4 km/h in still water and the river flows at 2 km/h, then in what direction must he swim to reach a point exactly opposite to the starting point and when will he reach it?
I have no idea how to solve this one.
Tan A = Y/X = 4/2 = 2.00.
A = 63.43o N. of E. = 26.57o E. of N.
Direction = 26.57o W. of N.
d = V*t = 0.6 km.
4*t = 0.6
t = 0.15 h. = 9 Min.
sin A=(2/4)=30 degree
time =s/v
600/root4^2-2^2
173.2seconds
To solve this problem, we need to use the concept of vector addition. The swimmer needs to navigate both across the river and against the current to reach a point opposite to the starting point.
First, let's calculate the time it would take for the swimmer to cross the river without the current. We can use the formula: Time = Distance / Speed.
The swimmer needs to cover a distance of 600m, but because his swimming speed is given in km/h, we need to convert the distance from meters to kilometers. Therefore, the swimmer needs to cover a distance of 0.6 km.
The speed of the swimmer in still water is given as 4 km/h, so the time taken to cross the river without the current is: Time = 0.6 km / 4 km/h = 0.15 hours (or 9 minutes).
Now let's calculate the downstream displacement caused by the river current during this time. The speed of the river current is given as 2 km/h, so the downstream displacement is: Downstream displacement = Speed of current * Time = 2 km/h * 0.15 hours = 0.3 km.
To reach a point opposite the starting point, the swimmer needs to compensate for this downstream displacement by swimming upstream (against the current) for the same amount of time. Thus, the swimmer should swim for an additional 9 minutes to counteract the current's effect and maintain his position.
To find the angle at which the swimmer must swim relative to the current, we can use the tangent function: Angle = arctan(Downstream displacement / Distance crossed).
In this case, the downstream displacement is 0.3 km and the distance crossed is 0.6 km. Therefore, the angle is: Angle = arctan(0.3 km / 0.6 km) = arctan(0.5) ≈ 26.56 degrees.
This means that the swimmer should swim at an angle of approximately 26.56 degrees upstream (against the current) to reach the opposite point.
To determine when the swimmer would reach the opposite point, we need to calculate the total time taken for the swim. Since the swimmer has already spent 9 minutes crossing the river without the current, the total time taken would be 9 minutes (to cross the river) + 9 minutes (to counteract the downstream displacement caused by the current) = 18 minutes.
Therefore, the swimmer will reach the exact opposite point 18 minutes after starting the swim.
Note: This solution assumes that the river flows in a straight line without any variations or meanders.