A person can row a boat at a rate of 25 m/s in still water. The person heads the boat directly across a stream that flows at a rate of 9 m/s. Find the resultant velocity of the boat.

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A person can row a boat at a velocity of 6 km/hr in still water. If the person heads upstream when the river flows downstream at a speed of 2 km/hr. Determine the magnitude and direction of the boat's resultant velocity.

20.5

To find the resultant velocity of the boat, we need to consider the velocity of the boat in still water and the velocity of the stream.

Let's define the velocity of the boat in still water as "v" and the velocity of the stream as "s".

Given:
Velocity of the boat in still water (v) = 25 m/s
Velocity of the stream (s) = 9 m/s

Now, the resultant velocity of the boat can be found using the concept of vector addition.

When the boat is moving directly across the stream, the resultant velocity will be the vector sum of the velocity of the boat in still water and the velocity of the stream.

Since the boat and stream are at right angles to each other, we can use the Pythagorean theorem to find the magnitude of the resultant velocity.

The magnitude of the resultant velocity (R) can be found by using the formula:
R = √(v^2 + s^2)

Substituting the given values:
R = √(25^2 + 9^2)

R = √(625 + 81)

R = √706

R ≈ 26.6 m/s

Therefore, the resultant velocity of the boat is approximately 26.6 m/s.