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

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) none

Tardigrade Admin · Accepted Answer

H = 5000 m = (uy2/2g) = (uy2/2× 10) uy2 = 100000 or uy = 100 √10 (m/s) ...(i) R = 20, 000 m = (2ux uy/g) = (2× ux/10) × 100√10 or ux = 100√10 ...(ii) Now, u = √ux2 + uy2 = 100√20 m/s

Q. 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

$7 m / s$

$14 m / s$

$28 m / s$

none

$H = 5000 m = \frac{u _{y}^{2}}{2 g}$
$= \frac{u _{y}^{2}}{2 \times 10}$
$u_{y}^{2} = 100000$
or $u_{y} = 10010 \frac{m}{s} ... (i)$
$R = 20, 000 m = \frac{2 u _{x} u _{y}}{g}$
$= \frac{2 \times u _{x}}{10} \times 10010$
or $u_{x} = 10010 ... (ii)$
Now, $u = u_{x}^{2} + u_{y}^{2}$
$= 10020 m / s$

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

7m/s

14m/s

28m/s