the velocity of boat in still water is 5 m/s.it crosses a river of width 60m always directed at angle 127.If velocity of river is 3.6m/s.find drift

To solve the problem of finding the drift of a boat crossing a river, we need to analyze the situation using some basic principles of physics, particularly vector addition. The boat's velocity in still water and the river's current both play crucial roles in determining how far downstream the boat will drift while crossing the river.

Understanding the Components

First, let's break down the information given:

• The velocity of the boat in still water is 5 m/s.
• The width of the river is 60 m.
• The angle at which the boat is directed is 127 degrees relative to the direction of the river flow.
• The velocity of the river current is 3.6 m/s.

Breaking Down the Boat's Velocity

To find the drift, we need to determine the effective components of the boat's velocity. Since the boat is directed at an angle, we can resolve its velocity into two components: one that is perpendicular to the river (across the width) and one that is parallel to the river (downstream).

Using trigonometry, we can find these components:

• The component of the boat's velocity across the river (perpendicular) is given by:

V_boat_perpendicular = V_boat * cos(θ)

• The component of the boat's velocity downstream (parallel) is given by:

V_boat_parallel = V_boat * sin(θ)

Calculating the Components

Here, θ = 127 degrees. We can calculate the components using the cosine and sine functions:

• V_boat_perpendicular = 5 m/s * cos(127°)
• V_boat_parallel = 5 m/s * sin(127°)

Using a calculator:

• cos(127°) ≈ -0.8387
• sin(127°) ≈ 0.5150

Now we can substitute these values:

• V_boat_perpendicular ≈ 5 * (-0.8387) ≈ -4.1935 m/s (this indicates the direction is upstream)
• V_boat_parallel ≈ 5 * 0.5150 ≈ 2.575 m/s

Effective Downstream Velocity

Now, we need to consider the river's current. The effective downstream velocity of the boat is the sum of the boat's downstream component and the river's velocity:

V_effective_downstream = V_boat_parallel + V_river

Substituting the values:

V_effective_downstream = 2.575 m/s + 3.6 m/s = 6.175 m/s

Time to Cross the River

Next, we need to determine how long it takes for the boat to cross the river. The time taken to cross can be calculated using the perpendicular component of the boat's velocity:

Time = Width of the river / V_boat_perpendicular

Since we need the absolute value of the perpendicular component (as we are only interested in the time), we take:

Time = 60 m / 4.1935 m/s ≈ 14.3 seconds

Calculating the Drift

Finally, we can find the drift, which is the distance the boat moves downstream during the time it takes to cross the river:

Drift = V_effective_downstream * Time

Substituting the values:

Drift = 6.175 m/s * 14.3 s ≈ 88.5 m

Final Result

The drift of the boat while crossing the river is approximately 88.5 meters downstream. This means that even though the boat is trying to go straight across, the current pushes it significantly downstream due to the combined effect of its velocity and the river's current.