Peggy drives from Cornwall to Atkins Glen in 35 min. Cornwall is 73.4 km from Illium in a direction 24° west of south. Atkins Glen is 25.1 km from Illium in a direction 13° south of west. Use Illium as your origin.
(a) Draw the initial and final position vectors. (Do this on paper. Your instructor may ask you to turn in this work.)
(b) Find the displacement during the trip.
magnitude_________km
direction_________° north of east
(c) Find Peggy's average velocity for the trip.
magnitude_________km/h
direction_________° north of east
I am so lost on this problem...I don't even know where to begin
You are going to have to do it on graph paper.
I have it graphed out, and I got the displacement in km, but I can't quite get the direction and the average velocity
No worries, I'm here to help! Let's break down the problem step by step.
(a) To start, let's draw the initial and final position vectors.
First, draw a plane representing the ground, and mark a point to represent Illium. Label it as point O.
From Illium, draw a vector 73.4 km long, in a direction 24° west of south. Label the end of this vector as point A.
Next, draw another vector 25.1 km long, in a direction 13° south of west. Label the end of this vector as point B.
Now, label point B as the final position. Your diagram should have three points: O (Illium), A (Cornwall), and B (Atkins Glen).
(b) Now let's find the displacement during the trip.
The displacement is a vector that points from the initial position (Illium) to the final position (Atkins Glen). In other words, it is the straight line connecting points O and B.
To find the magnitude of the displacement, you can use the distance formula or apply the Pythagorean theorem.
Magnitude of displacement = √((change in x)^2 + (change in y)^2)
(change in x) is the difference in x-coordinates between B and O. Similarly, (change in y) is the difference in y-coordinates.
To determine the direction of the displacement, you can use trigonometry. The angle formed between the positive x-axis and the displacement vector is the direction of the displacement.
(c) Lastly, we need to find Peggy's average velocity for the trip.
Average velocity is defined as the displacement divided by the time taken.
To find the magnitude of her average velocity, divide the magnitude of the displacement by the time taken (35 minutes).
To find the direction of the average velocity, you will need to use trigonometry to determine the angle formed between the positive x-axis and the velocity vector.
I hope this explanation helps you understand how to approach the problem! Let me know if you have any further questions.