A ship crosses a river aiming at the angle è to the left from the straight course. The speed of the ship with respect to water is v'. The width of the river is d and the water velocity is u to the right. What will be the side displacement h of the ship as it lands on the other shore?
Hmmmm. v' is respect to water....
That creates a really difficult problem, so I assume you don't mean that, but mean relative to still water.
Well, the velocity to the left is v'*sinTheta-u. I assume u is greater than the first term, so the velocity will be to the right.
Side displacement: figure the time across. d/v'costheta
then downstream distance d= velocity to right*time
To find the side displacement, h, of the ship as it lands on the other shore, you can use trigonometry.
Since the ship is aiming at an angle è to the left from the straight course, we can consider the angle between the direction of the ship's velocity (v') relative to the water, and the direction perpendicular to the shore.
Let's break down the velocity of the ship into its horizontal and vertical components:
- The horizontal component of the ship's velocity is v'cos(è) since the ship is aiming at an angle to the left.
- The vertical component of the ship's velocity is v'sin(è) since the ship is not aiming straight across the river.
Now, let's consider the vertical motion. The time, t, it takes for the ship to cross the river is the same as the time it takes for the ship to reach the other shore.
The vertical displacement, y, of the ship can be calculated using the formula: y = v'sin(è) * t.
Since the ship's velocity relative to water, v', is constant, and the time, t, it takes to cross the river is also constant, we can write t = d / (v'cos(è) + u). Here, d is the width of the river and u is the water velocity.
Now, substituting the value of t into the equation for y, we get: y = v'sin(è) * (d / (v'cos(è) + u)).
Finally, the side displacement, h, is given by h = y / sin(è) = v'sin(è) * (d / (v'cos(è) + u)) / sin(è).
Simplifying the equation, h = (v'd) / (v'cos(è) + u).
So, to find the side displacement, h, of the ship as it lands on the other shore, you can plug in the values of v', è, d, and u into the equation h = (v'd) / (v'cos(è) + u).