Question

A cannon fires a shell with a speed of $84m{s}^{-1}$. When the cannon is inclined at ${45}^o$, the horizontal distance covered is observed as $630m$. What is the percentage decrease in the horizontal distance observed due to air resistance.?

• A. 13
• B. 12.5
• C. 14
• D. 15

Answer 1

The correct option is B 12.5

The range projectile in the absence of air resistance, $R=\frac{u^2\sin 2\theta }{g}$
Horizontal speed $=u\cos \theta$

Time of flight $=\frac{2u\sin \theta }{g}$

therefore

$R=\frac{{84}^2\sin \left(2\times {45}^{\circ }\right)}{9.8}=720m$

Actual range observed $=630m$

Percentage decrease $=\frac{720-630}{720}\times 100=12.5\%$