A swimmer swims perpendicular to the bank of a 20.0 m wide river at a velocity of

1.3 m/s. Suppose the river has a current of 2.7 m/s [W].

(a) How long does it take the swimmer to reach the other shore?

(b) How far downstream does the swimmer land from his intended location?

how did you fins 41.5??

To solve this problem, we can use the concept of relative velocity. The swimmer's velocity relative to the riverbank is the vector sum of the swimmer's swimming velocity and the river's current velocity.

Let's break down the problem into two components: the horizontal component (perpendicular to the riverbank) and the vertical component (along the riverbank).

(a) To find the time it takes for the swimmer to reach the other shore, we need to calculate the time it takes for the swimmer to cover the horizontal distance of 20.0 m.

The horizontal component of the swimmer's velocity is unaffected by the river's current since it's perpendicular to the current. Therefore, the horizontal component remains at 1.3 m/s.

Time (t) = Distance (d) / Velocity (v)
t = 20.0 m / 1.3 m/s
t ≈ 15.38 seconds

So, it takes approximately 15.38 seconds for the swimmer to reach the other shore.

(b) To find how far downstream the swimmer lands from his intended location, we need to calculate the horizontal distance covered by the river's current during the time it took the swimmer to cross the river.

The horizontal component of the river's current velocity is 2.7 m/s, which is in the west direction. So, we need to find the distance covered westward in the time it took the swimmer (15.38 seconds).

Distance (d) = Velocity (v) × Time (t)
d = 2.7 m/s × 15.38 s
d ≈ 41.51 meters

Therefore, the swimmer lands approximately 41.51 meters downstream from his intended location.

In summary:
(a) It takes approximately 15.38 seconds for the swimmer to reach the other shore.
(b) The swimmer lands approximately 41.51 meters downstream from his intended location.

(2.7)(41.50)

=41.5

Well, let's dive into the calculations!

(a) To find the time taken to reach the other shore, we need to consider the swimmer's velocity and the river's current. Since the swimmer is swimming perpendicular to the river's bank, we can treat their velocities as vectors to find the resultant velocity.

The swimmer's velocity in the perpendicular direction remains unchanged, which is 1.3 m/s. However, we need to add the effect of the river's current, which is 2.7 m/s to the west.

To find the resultant velocity, we can use the Pythagorean theorem:

Resultant velocity = √(swimmer's velocity^2 + river's current velocity^2)
= √(1.3^2 + 2.7^2) m/s
≈ 2.9987 m/s

The swimmer needs to cross a 20.0 m wide river, so we can use the equation: Time = Distance / Velocity to find the time taken.

Time = 20.0 m / 2.9987 m/s
≈ 6.67 seconds

Therefore, it takes the swimmer approximately 6.67 seconds to reach the other shore.

(b) To find how far downstream the swimmer lands from their intended location, we can use the formula: Distance = Velocity × Time.

The swimmer's velocity perpendicular to the river's bank is 1.3 m/s, and the time taken to cross the river is 6.67 seconds. We need to find the downstream displacement caused by the river's current, which is 2.7 m/s.

Downstream displacement = Current velocity × Time
= 2.7 m/s × 6.67 s
≈ 18.02 meters

So, the swimmer lands approximately 18.02 meters downstream from their intended location.

Hope these calculations don't make you too "currently" confused!

X = -2.7 m/s.

Y = 1.3 m/s.
Q2.

a. Tan A = Y/X = 1.3/-2.7 = -0.48148.
A = -25.7 m/s = 25.7o N. of W. = 64.3o
W. of N. = Direction.

Vr = Sqrt(X^2 + Y^2) = Sqrt(2.7^2+1.3^2)= 3.0 m/s = Resultant velocity.

Dr = Sqrt(20^2 + 41.5^2) = 46.1 m. = Resultant distance.

Dr = Vr*T = 46.1 m.
T = 46.1/Vr = 46.1/3 = 15.4 s.

b. d = 20*Tan64.3 = 41.5 m. Downstream.