An ant walks on a piece of graph paper straight along the x axis a distance of 10.0 cm in 2.00 s. It then turns left 30.0 degrees and walks in a straight line another 10.0 cm in 1.90 s. Finally, it turns another 70.0 degrees to the left and walks another 10.0 cm in 1.40 s.

A. Determine the x component of the ant's average velocity.

*** I don't know how to find the x or y coordinates for this problem!!***

B. Determine the y component of the ant's average velocity.

C. Determine the magnitude of ant's average velocity.

D. Determine the direction of ant's average velocity.

I assume you have had some trignometry.

x component=10+10cos30 + 10cos(70+30)

go through that and make certain you understand it. I will be happy to check your y component.

I got the x-component to be: 10+8.66+3.42 which is 22.08.

But I also have to divide that by the total time that the ant traveled, right? So that time would be 5.3?

I got 4.166 when I divided it but the correct answer it supposed to be 3.19.

I really don't know how to get that answer. Could you please check my work please?

Well, the time is right, 5.3seconds.

The problem is, what is cosine100? It is negative right?

no

To solve this problem, we need to break down and analyze the ant's motion step by step. Let's start by finding the x and y coordinates for each step.

Step 1: Walking straight along the x-axis for 10.0 cm in 2.00 s
In this step, the ant only moves along the x-axis, so there is no change in the y-coordinate.

Step 2: Turning left 30.0 degrees and walking another 10.0 cm in 1.90 s
After turning left, the ant will have a component of motion in the y-direction as well.
To find the change in y-coordinate, we can use trigonometry. Since the ant turns left 30.0 degrees, we can represent the triangle formed by the ant's motion.

- The hypotenuse represents the distance the ant walks, which is 10.0 cm.
- The opposite side represents the change in y-coordinate.
- The adjacent side represents the change in the x-coordinate.

Using the trigonometric function sine, we can find the change in y-coordinate:
sin(30.0°) = opposite/hypotenuse
opposite = sin(30.0°) * 10.0 cm

Step 3: Turning another 70.0 degrees to the left and walking another 10.0 cm in 1.40 s
Again, we can use trigonometry to find the change in the x and y coordinates.
The change in x-coordinate can be found using cosine:
cos(70.0°) = adjacent/hypotenuse
adjacent = cos(70.0°) * 10.0 cm

The change in y-coordinate can be found using sine:
sin(70.0°) = opposite/hypotenuse
opposite = sin(70.0°) * 10.0 cm

Now, let's answer each part of the question:

A. Determine the x component of the ant's average velocity:
To find the x-component of the ant's average velocity, we need to calculate the total change in the x-coordinate and divide it by the total time taken.

Total change in x-coordinate = 10.0 cm (from step 1) + adjacent (from step 3)
Total time taken = 2.00 s (from step 1) + 1.40 s (from step 3)

The x-component of the ant's average velocity = Total change in x-coordinate / Total time taken

B. Determine the y component of the ant's average velocity:
The y-component of the ant's average velocity can be calculated using a similar approach.

Total change in y-coordinate = opposite (from step 2) + opposite (from step 3)
Total time taken = 1.90 s (from step 2) + 1.40 s (from step 3)

The y-component of the ant's average velocity = Total change in y-coordinate / Total time taken

C. Determine the magnitude of the ant's average velocity:
The magnitude of the ant's average velocity can be calculated using the formula:

Magnitude = sqrt((x-component of average velocity)^2 + (y-component of average velocity)^2)

D. Determine the direction of the ant's average velocity:
The direction of the ant's average velocity can be calculated using the inverse tangent function:

Direction = arctan((y-component of average velocity) / (x-component of average velocity))

By following these steps and using the given information, you can find the answers to parts A, B, C, and D of the question.