Question

A shell fired from a gun at sea level rises to a maximum height of $5\, km$ when fired at a ship $20 \,km$ away. The muzzle velocity should be

• A. $7 \,m/s$
• B. $14 \,m/s$
• C. $28 \,m/s$
• D. $56 \,m/s$

Answer 1

Answer: (D)

$56 \,m/s$

Answer 2

$H = 5000\,m = \frac{u_y^2}{2g}$
$= \frac{u_y^2}{2\times 10}$
$u_y^2 = 100000$
or $u_y = 100 \sqrt{10} \frac{m}{s}\,\,\,...(i)$
$R = 20, 000\,m = \frac{2u_x \,u_y}{g}$
$= \frac{2\times u_x}{10} \times 100\sqrt{10}$
or $u_x = 100\sqrt{10}\,\,\,...(ii)$
Now, $u = \sqrt{u_x^2 + u_y^2}$
$= 100\sqrt{20}\,m/s$