A boat is traveling on a bearing of 25 degrees East of North at a speed of 4 knots (a knot is 1.852 km/h). After traveling for 3 hours, the boats heading is changed to due South and it travels for an additional 2 hours at 5 knots. Using a Vector diagram, what is the resultant?
Why don't you use a vector diagram?
Hi, I am completely new to this, and missed a lot of classes due to hospital trips. Trying to cathc up but there is no sample question in my text. I don't really know how to get the numbers to make the vectors. Can you lead me in the right direction, would be very much appreciated, thank yo very much.
hi does someone answer you with your question?
To determine the resultant of the boat's motion, we need to break down its motion into its north-south (vertical) and east-west (horizontal) components.
Let's start by calculating the first leg of the boat's journey when it is traveling on a bearing of 25 degrees East of North for 3 hours at a speed of 4 knots.
The velocity of the boat can be calculated using the formula: velocity = speed × time.
So, the velocity of the boat during the first leg is 4 knots × 3 hours = 12 knots.
To calculate the vertical and horizontal components, we use trigonometric functions.
The vertical component V1 (north-south) is given by V1 = 12 knots × sin(25°).
The horizontal component H1 (east-west) is given by H1 = 12 knots × cos(25°).
Next, let's calculate the second leg of the boat's journey when it changes its heading to due South and travels for an additional 2 hours at a speed of 5 knots.
The velocity of the boat during the second leg is 5 knots × 2 hours = 10 knots.
The vertical component V2 (north-south) is given by V2 = 10 knots × cos(180°).
The horizontal component H2 (east-west) is given by H2 = 10 knots × sin(180°).
Now, let's find the resultant of the boat's motion by adding the vertical and horizontal components together.
The total vertical (north-south) component V_Total is given by V_Total = V1 - V2.
The total horizontal (east-west) component H_Total is given by H_Total = H1 + H2.
Using these values, we can draw a vector diagram to find the magnitude and direction of the resultant of the boat's motion.
Once we have the magnitudes of the vertical (north-south) and horizontal (east-west) components, we can use the Pythagorean theorem to find the magnitude of the resultant vector R, given by R = √(V_Total^2 + H_Total^2).
To find the direction of the resultant vector, we can use trigonometry. The angle θ is given by θ = arctan(H_Total / V_Total).
By finding the magnitude and direction of the resultant, we can determine the final position and direction of the boat after traveling for 3 hours on the first leg and 2 hours on the second leg.