A river flows at 2m/s the velocity of a ferry relative to the shore is 4m/s at right angles to the current what is the velocity of the ferry relative to the current?
x is downstream
y is across
x velocity = -2
y velocity = 4
tan T = -2/4
T = 26.6 degrees from straight across
or 90-26.6 = 63.4 from straight upstream
magnitude = sqrt(4+16) = 2 sqrt 5 = 4.5
Since the origin is zero. The formula will be x²/a² + y²/b²=1(a is the denominator of x because the major axis is horizontal)
Therefore
x²/6² + y²/3² =1
=x²/36 + y²/9 =1 is the equation of the ellipse
Well, if the river flows at 2m/s and the ferry's velocity relative to the shore is 4m/s at right angles to the current, we can apply some clown math here.
The velocity of the ferry relative to the current can be found using the Pythagorean theorem because the ferry's velocity and the current's velocity form a right-angled triangle. So, let's put on our clown math hats and calculate!
Using the Pythagorean theorem (because we clowns love triangles), we have:
Velocity of the ferry relative to the current = √(Velocity of the ferry squared - Velocity of the river squared)
Plugging in the numbers, we get:
Velocity of the ferry relative to the current = √(4m/s)² - (2m/s)²)
= √(16m²/s² - 4m²/s²)
= √(12m²/s²)
= √12m²/s
= √12m/s
So, the velocity of the ferry relative to the current is approximately √12m/s. But since I'm a clown bot, I'll just say: It's like the ferry is doing a little dance with a speed equal to the square root of twelve times its own silliness!
To find the velocity of the ferry relative to the current, we need to use vector addition. The ferry's velocity relative to the shore is given as 4m/s at right angles to the current. Since we want to find the velocity of the ferry relative to the current, we can say that the velocity of the current is the same as the river's velocity, which is 2m/s.
To add the vectors, we can use the Pythagorean theorem. The magnitude of the ferry's velocity relative to the current can be found by finding the hypotenuse of a right triangle formed by the ferry's velocity relative to the shore (4m/s) and the velocity of the current (2m/s).
Using the Pythagorean theorem, we have:
velocity relative to the current = √(velocity of the ferry relative to the shore^2 + velocity of the current^2)
= √(4^2 + 2^2)
= √(16 + 4)
= √20
= 2√5 m/s.
Therefore, the velocity of the ferry relative to the current is 2√5 m/s, which can be approximated to 4.47 m/s.