If H1 and H2 be the greatest heights of a projectile in two paths for a given value of range, then the horizontal range of projectile is given by

Question

If H1 and H2 be the greatest heights of a projectile in two paths for a given value of range, then the horizontal range of projectile is given by (A) ( H 1+ H 2/2) (B) ( H 1+ H 2/4) (C) 4 √H1 H2 (D) 4[ H 1+ H 2]

Tardigrade Admin · Accepted Answer

θ1+θ2=90° H1=(u2 sin 2 ω1/2 g) H2=(u2 sin (90°-θ1)/2 g) H1 H2=(R2/16) ∵ R=(u2 sin 2 θ1/g) R=4 √H1 H2

Q. If $H_{1}$ and $H_{2}$ be the greatest heights of a projectile in two paths for a given value of range, then the horizontal range of projectile is given by

$\frac{H _{1} + H _{2}}{2}$

$\frac{H _{1} + H _{2}}{4}$

$4 H_{1} H_{2}$

$4 [H_{1} + H_{2}]$

$θ_{1} + θ_{2} = 9 0^{\circ}$
$H_{1} = \frac{u ^{2} s i n ^{2} ω _{1}}{2 g}$
$H_{2} = \frac{u ^{2} s i n ( 9 0 ^{\circ} - θ _{1} )}{2 g}$
$H_{1} H_{2} = \frac{R ^{2}}{16}$
$∵ R = \frac{u ^{2} s i n ^{2} θ _{1}}{g}$
$R = 4 H_{1} H_{2}$

Q. If H1​ and H2​ be the greatest heights of a projectile in two paths for a given value of range, then the horizontal range of projectile is given by

2H1​+H2​​

4H1​+H2​​

4H1​H2​​

4[H1​+H2​]