A boat, which can travel 2.30m/s in still water is in a stream with a current moving at 1.20m/s. if the boat is pointed directly across the stream, determine the velocity of the boat relative to the shore?
sqrt(2.3^2+1.2^2)
it is a right triangle....
To determine the velocity of the boat relative to the shore, we need to consider the vector addition of the boat's velocity in still water and the current's velocity.
Let's break it down step by step:
1. The boat's velocity in still water is given as 2.30 m/s. This means that if there were no current, the boat would travel at a constant speed of 2.30 m/s.
2. The stream has a current moving at 1.20 m/s. This means that the current is pushing the boat in a specific direction with a speed of 1.20 m/s.
3. Since the boat is pointed directly across the stream, we can consider the stream's direction as perpendicular to the boat's direction.
4. Now, we can use vector addition to determine the boat's velocity relative to the shore. The boat's velocity relative to the shore is the resultant vector obtained by adding the boat's velocity vector and the current's velocity vector.
a. Draw a diagram or visualize a right-angled triangle with the boat's velocity vector as the hypotenuse (2.30 m/s) and the current's velocity vector as one of the perpendicular sides (1.20 m/s).
b. To find the remaining side (the other perpendicular side), we can use the Pythagorean theorem. Let's call this velocity V.
V² = (2.30 m/s)² - (1.20 m/s)²
V² = 5.29 m²/s² - 1.44 m²/s²
V² = 3.85 m²/s²
V = √(3.85 m²/s²)
V ≈ 1.96 m/s
5. So, the velocity of the boat relative to the shore is approximately 1.96 m/s. This means that when pointed directly across the stream, the boat will have a speed of 1.96 m/s and a direction perpendicular to the stream.
By following these steps, we can determine the velocity of the boat relative to the shore.
To determine the velocity of the boat relative to the shore, we can use vector addition.
The boat's velocity in still water is 2.30 m/s (let's call it Vboat), and the current's velocity is 1.20 m/s (let's call it Vcurrent).
Since the boat is pointed directly across the stream, the direction of the boat's velocity relative to the shore is perpendicular to the current's direction.
Using vector addition, we can find the boat's velocity relative to the shore (Vrelative) by creating a right-angled triangle:
Vrelative^2 = Vboat^2 + Vcurrent^2
Vrelative^2 = (2.30 m/s)^2 + (1.20 m/s)^2
Vrelative^2 = 5.29 m^2/s^2 + 1.44 m^2/s^2
Vrelative^2 = 6.73 m^2/s^2
Taking the square root of both sides:
Vrelative = √(6.73 m^2/s^2)
Vrelative ≈ 2.59 m/s
Therefore, the velocity of the boat relative to the shore is approximately 2.59 m/s.