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Consider a fraction a/b. If you go on decreasing the value of 'b' keeping 'a' constant the fraction starts increasing. Go on decreasing and the fraction approaches a large no. when you put a value close to zero it becomes larger. Thus when you divide it by zero the ans is so large that you can't count it, that is.....infinity.

The time can be divided into two - one for the descent(T1 )and the other(T2) for the sound to reach the observers ears. Thus T1 =

2h/g and T2 = h/v; Adding the two gives the result.

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No not necessarily. Gravitation and Electromagentic forces act beween bodies even if they are not in contact. A simple example is that of the earth and the sun. The sun attracts earth as a result of which it revolves round the sun. In turn the earth attracts the sun distorting its shape a little.(In reality this is how we determine planets outside our solar system. i.e, by measuring the distortion on the stars); Thus Newton's 3rd law is valid even if there is no contact b/w the bodies

Pls note that i'm using @ for theta
The equation of a projectile is y = tan@x - etc .etc.(Look some text books for that). Comparing with this eq. your eq. we see that the coefficent of x is tan@. Thus
tan@ =

3 which means that @ = 60;

If cot²A = cot(A-B)cot(A-C) show that cot2A = 1/2(cotB + cotC)

(1+sinA)/cosA + cos B/(1-sinB) = (2sinA - 2sinB)/(sin(A-B) + cosA - cosB)