https://file.aiquickdraw.com/mathbot/file/1727338958072v0idbffy.jpg

The image you provided shows a physics problem involving the position of a squirrel running in a park. The position vector \(\vec{r}(t)\) is given by:

\[
\vec{r}(t) = [(0.280 \, \text{m/s})t + (0.0360 \, \text{m/s}^2)t^2]\hat{i} + (0.0190 \, \text{m/s}^2)t^2\hat{j}
\]

The question asks for the \(v_y(t)\), the y-component of the velocity of the squirrel, as a function of time.

### Solution:
Velocity is the time derivative of the position vector \(\vec{r}(t)\). The y-component of the position is given by:

\[
y(t) = (0.0190 \, \text{m/s}^2)t^2
\]

To find \(v_y(t)\), differentiate \(y(t)\) with respect to time \(t\):

\[
v_y(t) = \frac{d}{dt}[(0.0190 \, \text{m/s}^2)t^2] = 2(0.0190 \, \text{m/s}^2)t = (0.0380 \, \text{m/s}^2)t
\]

Thus, the correct expression for \(v_y(t)\) is:

\[
v_y(t) = (0.0380 \, \text{m/s}^2)t
\]

It seems the correct answer is not exactly provided in the options, which may indicate a slight mismatch in the image or the options.

Do you want more details or have any other questions?

Here are some related questions you might find helpful:
1. What is the x-component \(v_x(t)\) of the squirrel’s velocity?
2. How would you calculate the acceleration \(a_y(t)\) from the velocity \(v_y(t)\)?
3. How do you find the speed (magnitude of velocity) at any time \(t\)?
4. What is the total displacement vector of the squirrel after time \(t\)?
5. How can you calculate the position vector \(\vec{r}(t)\) from given velocity components?

**Tip:** In physics problems involving vectors, differentiate the position vector to get velocity and differentiate velocity to get acceleration.

What is vy(t), the y-component of the velocity of the squirrel, as a function of time?

Learn how to find the y-component of the velocity of a squirrel running in a park based on its position vector. The position function includes time-dependent components, and solving the problem requires taking the derivative to find velocity. Suitable for college-level physics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation