Question 118: Motion in 2D & Vectors

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 -

Accepted Answer

Range will be same for time t
1
and t
2
, so angles of projection will be Ã¢ÂÂ$$	heta $$Ã¢ÂÂ & Ã¢ÂÂ90ÃÂ° Ã¢ÂÂ $$	heta $$Ã¢ÂÂ
$${t_1} = {{2u\sin 	heta } \over g}{t_2} = {{2u\sin \left( {{{90}^o} - 	heta } ight)} \over g}$$
and $$R = {{{u^2}\sin 2	heta } \over g}$$
$${t_1}{t_2} = {{4{u^2}\sin 	heta \cos 	heta } \over {{g^2}}} = {2 \over g}\left[ {{{2{u^2}\sin 	heta \cos 	heta } \over g}} ight]$$
= $${{2R} \over g}$$

Answer

$${{2R} \over g}$$

Answer

$${R \over g}$$

Answer

$${R \over {2g}}$$

Answer

$${R \over {4g}}$$

Motion in 2D & Vectors

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 -

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