A body is projected an angle theta with horizontal- Another body is projected with the same velocity an angle theta with the vertical- The ratio of the time of flights is-1 - 1displaystyle tan-2- theta -1displaystyle tan-2- 1 - thetadisplaystyle 1- cottheta

Question

Toppr Admin · Accepted Answer

-Let time of first and-second projectiles are t1-xA0-and-xA0-t2 respectively-t1-2usin-x3B8-gt2-2usin-90-x2212-x3B8-g-2ucos-x3B8-gt1t2-2usin-x3B8-g2ucos-x3B8-g-sin-x3B8-cos-x3B8-1cot-x3B8-

A body is projected at an angle $θ$ with horizontal. Another body is projected with the same velocity at an angle $θ$ with the vertical. The ratio of the time of flights is-
$1 : 1$
$t a n^{2} θ : 1$
$t a n^{2} 1 : θ$
$1 : c o t θ$

Let time of first and second projectiles are $t_{1} a n d t_{2}$ respectively.

$t_{1} = \frac{2 u s i n θ}{g} t_{2} = \frac{2 u s i n (90 - θ)}{g} = \frac{2 u c o s θ}{g} \frac{t_{1}}{t_{2}} = \frac{\frac{2 u s i n θ}{g}}{\frac{2 u c o s θ}{g}} = \frac{s i n θ}{c o s θ} = \frac{1}{c o t θ}$

A body is projected at an angle θ with horizontal. Another body is projected with the same velocity at an angle θ with the vertical. The ratio of the time of flights is-1:1tan2θ:1tan21:θ1:cotθ

Let time of first and second projectiles are t1 and t2 respectively. t1=2usinθgt2=2usin(90−θ)g=2ucosθgt1t2=2usinθg2ucosθg=sinθcosθ=1cotθ

A body is projected at an angle $θ$ with horizontal. Another body is projected with the same velocity at an angle $θ$ with the vertical. The ratio of the time of flights is-
$1 : 1$
$t a n^{2} θ : 1$
$t a n^{2} 1 : θ$
$1 : c o t θ$