Question

Ratio of minimum kinetic energies of two projectiles of same mass is $4:1$ . The ratio of the maximum height attained by them is also $4:1$ . The ratio of their ranges would be

• A. $16:1$
• B. $4:1$
• C. $8:1$
• D. $2:1$

Answer 1

Answer: (B)

Minimum kinetic energies are at highest point
$\frac{\frac{1}{2}m{u}_1^{2}co{s}^2{\theta }_1}{\frac{1}{2}m{u}_2^{2}co{s}^2{\theta }_2}=\frac{4}{1}$
$\Rightarrow \frac{u_{1}cos{\theta }_1}{u_{2}cos{\theta }_2}=2$ ......(1)
and ratio of the maximum height
$\frac{u_1^{2}si{n}^2{\theta }_1}{u_2^{2}si{n}^2{\theta }_2}=\frac{4}{1}$
or $\frac{u_{1}sin{\theta }_1}{u_{2}sin{\theta }_2}=\frac{2}{1}$ ...(2)
from equation no. (1) and (2)
$\frac{u_{1}sin{\theta }_1.u_{1}cos{\theta }_1}{u_{2}sin{\theta }_2.u_{2}cos{\theta }_2}=\frac{4}{1}$
$\frac{\frac{g{R}_1}{2}}{\frac{g{R}_2}{2}}=\frac{4}{1}$
$\Rightarrow \frac{R_1}{R_2}=\frac{4}{1}$