Question

The kinetic energy of a projectile at its highest position is $K$. If the range of the projectile is four times the height of the projectile, then the initial kinetic energy of the projectile is

• A. $\sqrt{2}K$
• B. $2K$
• C. $4K$
• D. $2\sqrt{2}K$

Answer 1

Answer: (B)

$2K$

At highest point,
$\frac{1}{2}m{u}_x^2=K$

$\therefore u_x=\sqrt{\frac{2K}{m}}$

$R=4H$

$\frac{2u_x{u}_y}{g}=\frac{4u_y^2}{2g}$

$\therefore u_y=u_x=\sqrt{\frac{2K}{m}}$

Now, $K_i=\frac{1}{2}m{u}^2=\frac{1}{2}m(u_x^2+u_y^2)$

$=\frac{1}{2}m(\frac{2K}{m}+\frac{2K}{m})$

$=2K$