A filmmaker wants to achieve an interesting visual effect by filming a scene through a converging lens with a focal length of 52.0 m. The lens is placed betwen the camera and a horse, which canters toward the camera at a constant speed of 7.4 m/s. The camera starts rolling when the horse is 40.0 m from the lens. Find the average speed of the image of the horse (a) during the first 2.0 s after the camera starts rolling and (b) during the following 2.0 s.

To find the average speed of the image of the horse, we need to determine the distance traveled by the image in a given time period.

(a) During the first 2.0 s after the camera starts rolling:
1. First, we need to find out where the lens forms the image of the horse.
- The lens forms an image using the lens formula, which is given by 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance from the lens.
- Plugging in the values, we get 1/52.0 = 1/v - 1/40.0. Rearranging the equation gives us:
1/v = 1/52.0 + 1/40.0.
Calculating this, we find v ≈ 22.86 m.

2. Next, we calculate the initial speed of the image.
- The initial distance between the horse and the lens is 40.0 m. As the image of the horse is 22.86 m behind the lens, the initial distance between the horse and the image is 40.0 m + 22.86 m = 62.86 m.
- To find the initial speed of the image, we divide this initial distance by the time taken, which is 2.0 s:
Initial speed = 62.86 m / 2.0 s = 31.43 m/s.

(b) During the following 2.0 s:
1. For the next 2.0 s, the distance between the horse and the image decreases as the horse moves closer to the lens.
- The horse's speed is given as 7.4 m/s, so in 2.0 s, the horse travels 7.4 m/s × 2.0 s = 14.8 m.
- As the horse travels toward the lens, the distance between the horse and the lens decreases by 14.8 m, causing the distance between the horse and the image to decrease by the same amount.

2. To find the final distance between the horse and the image, we subtract the distance traveled by the horse from the initial distance between them.
- The initial distance between the horse and the image was 62.86 m. Subtracting the distance traveled by the horse, we get 62.86 m - 14.8 m = 48.06 m.

3. Finally, we calculate the average speed of the image during the following 2.0 s by dividing the final distance by the time taken:
Average speed = (48.06 m - 22.86 m) / 2.0 s = 12.10 m/s.

So, the average speed of the image of the horse is:
(a) 31.43 m/s during the first 2.0 s after the camera starts rolling.
(b) 12.10 m/s during the following 2.0 s.