A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t 1 and t 2 are the values of the time taken by it to hit the target in two possible ways, the product t 1 t 2 is:

Step-by-step solution

We know for complementary angle range is same for same projection speed. t 1 = 2 u s i n ( θ ) g ….. (i) t 2 = 2 u s i n ( 90 - θ ) g ….. (ii) R = 2 u 2 s i nθc o s θ g .… (iii) From equation (i) and (ii) t 1 t 2 = 4   U 2 s i n θ   c o s θ g 2 (Using the value of R from equation iii) t 1 t 2 = 2 R g