A car is moving rectilinearly on a horizontal path with acceleration `a_(0)`.A person sitting inside the car observes that an insect `S` is crawling up the screen with an acceleration a.If `theta` is the inclination of the wind screen with the horizontal, then the acceleration of the insect.

Options

A. parallel to screen is `a+a_(0) cos theta`
B. along the horizontal is `a_(0)-a cos theta`
C. perpendicular to screen is `a_(0)sin theta`
D. perpendicular to screen is `a_(0) tan theta`

Answer

To solve the problem, we need to analyze the motion of the insect as observed from the car. We will break down the accelerations into components based on the inclination of the windscreen.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The car is moving with an acceleration \( a_0 \).
- The insect is crawling up the screen with an acceleration \( a \).
- The angle of inclination of the windscreen with the horizontal is \( \theta \).

2. **Draw a Diagram:**
- Visualize the car moving horizontally and the windscreen inclined at an angle \( \theta \).
- Mark the direction of the car's acceleration \( a_0 \) and the insect's acceleration \( a \).

3. **Resolve the Accelerations:**
- The acceleration of the car \( a_0 \) can be resolved into two components:
- **Horizontal Component:** \( a_0 \cos \theta \)
- **Vertical Component:** \( a_0 \sin \theta \)
- The acceleration of the insect \( a \) can also be resolved into components:
- **Horizontal Component:** \( a \cos \theta \)
- **Vertical Component:** \( a \sin \theta \)

4. **Set Up the Equations:**
- Since the observer inside the car sees the insect moving, we can set up the following equations based on the components:
- **Horizontal Direction:** The net acceleration in the horizontal direction as observed from the car is:
\[ a_{\text{horizontal}} = a_0 - a \cos \theta \]
- **Vertical Direction:** The net acceleration in the vertical direction is:
\[ a_{\text{vertical}} = a - a_0 \sin \theta \]

5. **Determine the Resultant Acceleration:**
- The resultant acceleration of the insect as observed from the car can be calculated using the Pythagorean theorem:
\[ a_{\text{insect}} = \sqrt{(a_0 - a \cos \theta)^2 + (a - a_0 \sin \theta)^2} \]

6. **Conclusion:**
- The acceleration of the insect as observed by the person in the car is given by the resultant of the horizontal and vertical components derived above.