Question

Two stones are projected with same velocity $v$ at an angle $\theta \&(90-\theta ).$ If $H$ and $H_1$ are the greatest heights in the two paths, what is the relation between $R,H$ and $H_1?$

• A. $R=4\sqrt{H{H}_1}$
• B. $R=\sqrt{H{H}_1}$
• C. $R=4H{H}_1$
• D. None of the above

Answer 1

Answer: (A)

Range of projectile
$R=\frac{2u^2\sin \theta \cos \theta }{g}\dots$(1)
Height $H=\frac{u^2{\sin }^2\theta }{2g}\dots$(2)
$H_1=\frac{u^2{\sin }^2(90-\theta )}{2g}=\frac{u^2{\cos }^2\theta }{2g}\dots$(3)
Then, $H{H}_1=\frac{u^2{\sin }^2\theta u^2{\cos }^2\theta }{2g2g}\dots$(4)
From Eq. (1), we get
$R^2=\frac{4u^2{\sin }^2\theta u^2{\cos }^2\theta \times 4}{2g\times 2g}$
$R=\sqrt{16H{H}_1}$ [from Eq. $(4)]$
$=4\sqrt{H{H}_1}$