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

Question

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:

TestHub · Accepted Answer

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

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