Question

Two bodies are thrown with the same initial velocity at angles $\alpha$ and $({90}^o-\alpha )$ with the horizontal. What will be the ratio of i)maximum heights attained by them and ii)of horizontal ranges.

Answer 1

• maximum height attained by projectile is ,$H=\frac{u^2\sin \theta }{2g}$
  

so, ratio, $\frac{H_1}{H_2}=\frac{\sin \alpha }{\sin ({90}^0-\alpha )}=\frac{\sin \alpha }{\cos \alpha }=\tan \alpha$

• Range is given by, $R=\frac{u^2\sin 2\theta }{g}$

so ratio in both case, $\frac{R_1}{R_2}=\frac{\sin 2\alpha }{\sin 2({90}^0-\alpha )}=\frac{\sin 2\alpha }{sin({180}^0-2\alpha )}=\frac{sin2\alpha }{\sin 2\alpha }=1$

so, $R_1=R_2$