Michaela is planning a trip in Ireland from Killarney to Cork to visit Blarney Castle. She also wants to visit Fermoy which is located 86 km due east of Killarney and 27 km due north of Cork. Draw the displacement vectors for the trip when she travels from Killarney to Fermoy to Cork.
(a) What is the magnitude of her displacement once she reaches Cork? put in (km)
(b) How much additional distance does Michaela travel in going to Cork by way of Fermoy instead of going directly from Killarney to Cork?
right triangle start at Killarney
horizontal leg = 86 East (+x) to Femroy
vertical leg = 27 South (-y) from Femroy
sum = 86 + 27
going directly = sqrt (86^2+27^2)
(the hypotenuse)
To answer these questions, we need to analyze the displacement vectors for Michaela's trip. Let's break it down step by step:
1. Start by drawing a map with the three locations: Killarney, Fermoy, and Cork.
2. Draw a vector from Killarney to Fermoy, representing the displacement between these two locations. Given that Fermoy is located 86 km east of Killarney, draw a vector in that direction.
3. Draw a vector from Fermoy to Cork, representing the displacement between these two locations. Given that Fermoy is located 27 km north of Cork, draw a vector in that direction.
4. The displacement vector from Killarney to Cork can be found by adding these two vectors together. You can do this by placing the tail of the second vector (Fermoy to Cork) at the head of the first vector (Killarney to Fermoy) and drawing a new vector from the tail of the first vector to the head of the second vector. This new vector represents the displacement from Killarney to Cork.
Now that we have the displacement vector from Killarney to Cork, we can answer the questions:
(a) The magnitude of this displacement vector represents the distance between Killarney and Cork. Measure the length of the displacement vector on your map and convert it to kilometers. That will give you the magnitude of her displacement once she reaches Cork.
(b) To determine the additional distance traveled by going to Cork via Fermoy instead of directly from Killarney to Cork, you need to compare the length of the displacement vector from Killarney to Cork (found in part (a)) with the straight-line distance between Killarney and Cork. Measure this straight-line distance on your map and convert it to kilometers. The difference between these two values will give you the additional distance Michaela traveled by going through Fermoy.
Remember to use the scale on your map to make accurate measurements and conversions.