An athlete crosses a 21 m wide river by swimming perpendicular to the water current at a speed of 1.1 m/s relative to the water.
How fast is the water in the river flowing with respect to the ground in m/s?
How long did it take him to get across? More information is needed.
This is online homework. This is all the information given with Part B asking the speed of the swimmer.
To determine the speed of the water in the river with respect to the ground, we can use the concept of relative velocity.
Let's assume the speed of the water current is denoted as Vw (in m/s) and the speed of the athlete relative to the ground is denoted as Va (in m/s).
Since the athlete is swimming perpendicular to the water current, the horizontal component of their velocity should be the same as the speed relative to the ground. Therefore, Va = 1.1 m/s.
To cross the river, the athlete needs to compensate for the water current by swimming at an angle. The resultant velocity, which is the combination of their swimming speed and the water current, must be perpendicular to the direction of the riverbank.
We can use the Pythagorean theorem to relate the velocity of the athlete with respect to the ground (Va) and the velocity of the water current (Vw).
The resultant velocity is given by:
Vr^2 = Va^2 + Vw^2
As the athlete swims perpendicular to the water current, the resultant velocity (Vr) is 1.1 m/s.
Plugging in the values, we get:
(1.1 m/s)^2 = (Vw)^2 + (1.1 m/s)^2
Simplifying the equation, we have:
(1.1 m/s)^2 - (1.1 m/s)^2 = (Vw)^2
0 = (Vw)^2
Vw = 0 m/s
Therefore, the water in the river is flowing at a speed of 0 m/s relative to the ground. This implies that the river is not flowing in the horizontal direction.