A ship is sailing due east at 18 knots runs into a 3 knot current moving 40 East of North.
The resultant speed an direction of the ship are:
good
A ship travelling due West at 16 knots runs into a current moving at 4 knots due
South. Find the resultant and direction of the ship.
Well, let's see... If the ship is sailing due east at 18 knots and runs into a 3 knot current moving 40° East of North, we can calculate the resultant speed and direction using some trigonometry and a touch of humor.
First, we need to break down the ship's velocity into its components: eastward (18 knots) and northward (0 knots).
Now, let's focus on the current. It's moving 40° East of North, so we'll use some math magic (and a pinch of clown humor) to determine its eastward and northward components.
If the current is moving 40° East of North, then we can imagine it as a clown doing a silly dance move. It's like saying the current is moving "NorthEast-ish".
Now, let's break down the current's velocity into its components. As the current is moving "NorthEast-ish", we can consider it as a combination of northward and eastward motion. However, since we don't know the exact angle or magnitude of the current's velocity, we can't calculate its components accurately.
But fear not! This is where the clown's magic comes in. Since we know the current has a magnitude of 3 knots, we can use a little bit of clown logic and pretend that the current is moving only northward at 3 knots. It's like the other clown just decided to "tango" in a straight line.
Now, we can add up the eastward and northward components separately to find the resultant speed and direction of the ship. But remember, this is all just a clown show, so take the results with a grain of silly laughter.
Adding the eastward components, we have:
Ship's eastward velocity: 18 knots
Current's eastward velocity (improvised): 0 knots
Adding the northward components, we have:
Ship's northward velocity: 0 knots
Current's northward velocity (improvised): 3 knots
Now, let's calculate the resultant speed using Pythagoras (but with a clown twist). The hypotenuse (resultant speed) is given by the square root of the sum of the squares of the eastward and northward components (clown music playing in the background).
Resultant speed = √((18^2) + (3^2)) = √(324 + 9) = √333 ≈ 18.25 knots
Voila! The resultant speed of the ship is approximately 18.25 knots.
As for the direction, we can use some clown geometry to determine it. Since the current is improvising its dance moves and pretending to only move northward, we can visualize that the resultant velocity vector (ship's velocity vector + current's improvised velocity vector) points slightly northeast.
So, to summarize the resultant speed and direction of the ship sailing due east at 18 knots running into a 3 knot current moving 40° East of North, we have:
Resultant speed: Approximately 18.25 knots
Resultant direction: Northeast-ish (clown approved!)
Remember, this calculation involved a lot of clown logic and improvisation, so take the results with a smile and a chuckle!
To determine the resultant speed and direction of the ship, we need to use vector addition.
Step 1: Convert the given speeds into vector form.
The ship is traveling due east at 18 knots, so its velocity vector can be represented as 18i^ (where i^ is the unit vector in the eastward direction).
The current is moving 40° east of north with a speed of 3 knots. First, determine the northward and eastward components of the current's velocity.
The northward component = 3 * sin(40°) = 1.93 knots (approx.)
The eastward component = 3 * cos(40°) = 2.29 knots (approx.)
So, the current's velocity vector can be represented as 2.29i^ + 1.93j^ (where j^ is the unit vector in the northward direction).
Step 2: Add the ship's velocity vector to the current's velocity vector.
To add these vectors, simply add their corresponding components.
Resultant velocity vector = (18i^) + (2.29i^ + 1.93j^)
= (18 + 2.29)i^ + 1.93j^
= 20.29i^ + 1.93j^
Step 3: Determine the magnitude and direction of the resultant velocity.
The magnitude of the resultant velocity can be found using the Pythagorean theorem:
Resultant speed = sqrt((20.29)^2 + (1.93)^2) knots
= 20.85 knots (approx.)
The direction of the resultant velocity can be found using trigonometry:
Resultant direction = atan(1.93/20.29)°
= 5.42° (approx.)
Therefore, the resultant speed of the ship is approximately 20.85 knots, and its direction is approximately 5.42 degrees east of due east.
obtained by adding the two vectors:
(18,0)+(3cos(40),3sin(40))
=(18+3cos(40), 3sin(40))
=(x,y)
The resultant speed R is obtained by
|R|=sqrt(x²+y²)