Final answer:
Calculation of focal length and image size requires the use of lens and magnification equations to determine the distance from the lens to the film and what fraction of the person will be captured within the image.
Step-by-step explanation:
The question involves calculating the focal length of a camera lens and the size of the image produced by the lens. When a camera with a 50.0 mm focal length lens photographs a person standing 3.00 m away, the distance from the lens to the film (a) can be determined using the lens equation 1/f = 1/d_o + 1/d_i, where d_o is the distance of the object from the lens, and d_i is the distance of the image from the lens.
For (b), the magnification equation m = -d_i/d_o can be used to find the size of the image on the film and what fraction of the person will fit.
The question is asking about the distance fallen by a lens cap dropped by Rochelle. The distance fallen by an object in free fall can be calculated using the equation d = ½gt², where d is the distance fallen, g is the acceleration due to gravity (approximately 9.8 m/s²), and t is the time in seconds. Therefore, the correct answer is (a) 4.9t² meters.