If a man is able to row at 5m/s in still water and he points his boat at a 50 degree angle from the shore in an upstream direction in a river that's flowing at 4 m/s how far, either up or downstream will be land on the other side of the river if the river is 45n across?

Question

If a man is able to row at 5m/s in still water and he points his boat at a 50 degree angle from the shore in an upstream direction in a river that's flowing at 4 m/s how far, either up or downstream will be land on the other side of the river if the river is 45n across?

Answer 1

Vb = 5m/s[90o+50o] + 4m/s.

Vb =(5*Cos140+4) + (5*sin140)i,
Vb = 0.170 + 3.21i = 3.214/m/s[87o].

Tan(90-87) = d/45.
Tan3 = d/45, d = ?.

Answer 2

To determine how far the man will land on the other side of the river, we first need to break down the velocities into horizontal and vertical components.

Let's consider the man's velocity in still water (5 m/s) and the river's velocity (4 m/s). Since the man is aiming at a 50-degree angle, we can decompose his velocity into horizontal and vertical components using trigonometry.

The horizontal component of the man's velocity, Vh, can be calculated as follows:
Vh = V * cos(θ)
where V is the magnitude of the total velocity (5 m/s) and θ is the angle (50 degrees). Plugging in the values:
Vh = 5 * cos(50°) ≈ 5 * 0.6428 ≈ 3.214 m/s

The vertical component of the man's velocity, Vv, can be found similarly:
Vv = V * sin(θ)
Vv = 5 * sin(50°) ≈ 5 * 0.766 ≈ 3.830 m/s

Since the river is flowing upstream, the effective velocity of the man in the upstream direction will be reduced:
Upstream velocity = Vh - River velocity
Upstream velocity = 3.214 m/s - 4 m/s = -0.786 m/s

Now we can find out how long it will take for the man to cross the river. Let's assume the time taken is "t" seconds.

The distance traveled by the man across the river (in the upstream direction) is given by:
Distance = Upstream velocity * t

The man wants to reach the other side of a 45-meter wide river. So, the distance traveled is equal to the width of the river (45 meters).

Distance = Upstream velocity * t = 45 meters

Solving for "t":
t = Distance / Upstream velocity
t = 45 meters / -0.786 m/s ≈ - 57.29 seconds (Note: The negative sign indicates the direction is opposite to that of the river flow)

Since time cannot be negative, we can take the absolute value of "t":
t = abs(-57.29 seconds) ≈ 57.29 seconds

Therefore, it would take approximately 57.29 seconds for the man to cross the river and land on the other side, traveling in an upstream direction.

If a man is able to row at 5m/s in still water and he points his boat at a 50 degree angle from the shore in an upstream direction in a river that's flowing at 4 m/s how far, either up or downstream will be land on the other side of the river if the river is 45n across?

It's 4

Vb = 5m/s[90o+50o] + 4m/s.

To determine how far the man will land on the other side of the river, we first need to break down the velocities into horizontal and vertical components.