If the speed of light in air is 3.00 times 10 to the 8 m/s power and the speed of light in water is 2.25 times 10 to the 8 power
m/s what is the index of refraction of water
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This question needs research to be answered. From the given information alone it can't be answered without making wild assumptions.
Ideally, you need to take a look at a distribution (or a histogram) of asteroid diameters, identify the "mode" of such a distribution, and find the corresponding diameter. That value will be the answer.
I am attaching one such histogram on asteroid diameters from the IRAS asteroid catalog I could find online. (In order to get a single histogram, you need to add the individual curves in the figure first). Eyeballing this sample, I'd say the mode is somewhere around 10km, so the answer would be: the diameter of most asteroid from the IRAS asteroid catalog is about 10km.
Answer: (a) t1 = omega1/alpha
(b) theta1 = 1/2 * alpha*theta1^2
(c) t2 = omega2/5*alpha
Explanation: see attachment
