https://file.aiquickdraw.com/mathbot/file/172727395590406ami84b.jpg

Let's go through the problem step by step.

We are given:
- Initial velocity \( v = 20 \, \text{m/s} \),
- Time of travel \( t = 5 \, \text{seconds} \),
- Angle \( \theta = 35^\circ \).

### Part A: How fast did they drive in the x-direction?
The horizontal (x-direction) component of velocity can be found using:
\[
v_x = v \cdot \cos(\theta)
\]
\[
v_x = 20 \cdot \cos(35^\circ)
\]
Let me calculate this.

### Part B: How fast did they drive in the y-direction?
The vertical (y-direction) component of velocity is:
\[
v_y = v \cdot \sin(\theta)
\]
\[
v_y = 20 \cdot \sin(35^\circ)
\]
I'll calculate this as well.

### Part C: How far did they drive at 35°?
The total displacement is given by:
\[
d = v \cdot t
\]
\[
d = 20 \, \text{m/s} \cdot 5 \, \text{s} = 100 \, \text{m}
\]

### Part D: How far did they drive in the x-direction?
The displacement in the x-direction can be found by:
\[
d_x = v_x \cdot t
\]
We will use the value of \( v_x \) from part A.

### Part E: How far did they drive in the y-direction?
Similarly, for the y-direction:
\[
d_y = v_y \cdot t
\]
We will use the value of \( v_y \) from part B.

### Part F: Draw the triangle that shows the displacement of the car.
This will involve showing the horizontal and vertical displacements forming the two legs of the triangle, with the total displacement as the hypotenuse.

Let me compute the values for parts A, B, D, and E now.Here are the results for the parts calculated:

### Part A: 
The speed in the x-direction is approximately \( 16.38 \, \text{m/s} \).

### Part B:
The speed in the y-direction is approximately \( 11.47 \, \text{m/s} \).

### Part D:
The displacement in the x-direction is approximately \( 81.92 \, \text{m} \).

### Part E:
The displacement in the y-direction is approximately \( 57.36 \, \text{m} \).

To summarize the remaining parts:
- **Part C**: The total distance traveled at 35° is 100 meters.
- **Part F**: The triangle consists of:
  - Horizontal leg (x-displacement): \( 81.92 \, \text{m} \),
  - Vertical leg (y-displacement): \( 57.36 \, \text{m} \),
  - Hypotenuse (total displacement): \( 100 \, \text{m} \).

Would you like a visual for the triangle or further clarification?

---

### Relative questions:
1. What is the relationship between angle and velocity components?
2. How would increasing the angle affect the horizontal and vertical velocities?
3. What trigonometric functions are used to resolve velocities into components?
4. How can we find the resultant displacement if the velocities are different?
5. What is the role of time in determining displacements?

**Tip**: In projectile motion, the angle directly influences the balance between horizontal and vertical velocity.

A car drives 20 m/s for 5 seconds at 35°. How fast did they drive in the x-direction? How fast did they drive in the y-direction? How far did they drive at 35°? How far did they drive in the x-direction? How far did they drive in the y-direction? Draw the triangle that shows the displacement of the car.

Solve a physics problem where a car drives at 20 m/s for 5 seconds at a 35° angle. Learn how to calculate velocity components, total displacement, and represent the displacement with a triangle. Suitable for high school students in Grades 9-12.

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