Question

Two projectiles are thrown at angles $\Theta$ and ( ${90}^{\circ }\Theta$) with same speed. The ratio of their horizontal ranges are

• A. 1 : 1
• B. 1 : tan $\Theta$
• C. tan $\Theta$: 1
• D. $ta{n}^2\Theta :1$

Answer 1

The correct option is A 1 : 1

For $\theta ;$ Horizontal range, $R_1=\frac{V^2\sin 2\theta }{g}$

for $(90-\theta );R_2=\frac{V^2{\sin }^2(90-\theta )}{g}$

$=\frac{V^2\sin (180-2\theta )}{g}$

$=\frac{V^2\sin 2\theta }{g}$

$\Rightarrow R_1=R_2$

Hence, the answer is $1:1.$