Question

A cannon at the ground fires a shell at speed of 50 km/hr. If the angle of projection is $ 30{}^\circ , $ the range of the shell (take $ g=10\text{ }m/{{s}^{2}} $ ) is, in km.

• A. $ 2.5\sqrt{{}}3 $
• B. $ 62.5\sqrt{{}}3 $
• C. $ 125\sqrt{{}}3 $
• D. $ 9.65\sqrt{{}}3\times {{10}^{-3}} $

Answer 1

Answer: (D)

: Range of projectile $ =R=\frac{{{u}^{2}}\sin 2\theta }{g} $ $ \therefore $ $ R={{\left( \frac{50\times 1000}{60\times 60} \right)}^{2}}\times \frac{\sin 60{}^\circ }{10} $ Or $ R=\frac{125\times 125\times \sqrt{3}}{9\times 9\times 2\times 10}m $ Or $ R=9.65\sqrt{3}m $ Or $ R=9.65\sqrt{3}\times {{10}^{-3}}km $