Question

Two objects are projected with same velocity ' $u$ ' however at different angles $\propto$ and $\beta$ with the horizontal If $\alpha+\beta=90^{\circ}$, the ratio of horizontal range of the first object to the 2nd object will be :

• A. $1:2$
• B. $4: 1$
• C. $2: 1$
• D. $1:1$

Answer 1

The Correct Option is D

The correct answer is (D) : $1:1$
$\text{Range}=\frac{u^2\sin 2\theta }{g}$
Range for projection angle " $\alpha$ "
$R_1=\frac{u^2\sin 2\alpha }{g}$
Range for projection angle " $\beta$ "
$R_2=\frac{u^2\sin 2\beta }{g}$
$\alpha +\beta =90^{\circ }\text{(Given)}$
$\Rightarrow \beta =90^{\circ }-\alpha$
$R_2=\frac{u^2\sin 2\left(90^{\circ }-\alpha \right)}{g}$
$R_2=\frac{u^2\sin \left(180^{\circ }-2\alpha \right)}{g}$
$R_2=\frac{u^2\sin 2\alpha }{g}$
$\Rightarrow \frac{R_1}{R_2}=\frac{\left(\frac{u^2\sin 2\alpha }{g}\right)}{\left(\frac{u^2\sin 2\alpha }{g}\right)}=\frac{1}{1}$