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3-2.Motion in Plane
easy
Two projectiles $A$ and $B$ are thrown with initial velocities of $40\,m / s$ and $60\,m / s$ at angles $30^{\circ}$ and $60^{\circ}$ with the horizontal respectively. The ratio of their ranges respectively is $\left( g =10\,m / s ^2\right)$
A$\sqrt{3}: 2$
B$2: \sqrt{3}$
C$1:1$
D$4:9$
(JEE MAIN-2023)
Solution
$R_1=\frac{u_1^2 \sin 2 \theta_1}{ g } ; R_2=\frac{ u _2^2 \sin 2 \theta_2}{ g }$
$\frac{R_1}{R_2}=\frac{u_1^2}{u_2^2} \frac{\sin 2 \theta_1}{\sin 2 \theta_2}=\frac{40^2 \sin \left(2 \times 30^{\circ}\right)}{60^2 \sin \left(2 \times 60^{\circ}\right)}=\frac{4}{9}$
$\frac{R_1}{R_2}=\frac{u_1^2}{u_2^2} \frac{\sin 2 \theta_1}{\sin 2 \theta_2}=\frac{40^2 \sin \left(2 \times 30^{\circ}\right)}{60^2 \sin \left(2 \times 60^{\circ}\right)}=\frac{4}{9}$
Standard 11
Physics
