Question

The ceiling of a tunnel is 5m high. What is the maximum horizontal distance that a ball thrown in a projectile with a speed of 2$0m{s}^{-1}$ can go without hitting the ceiling of the tunnel? $(g=10m{s}^{-2})$

• A. $10\sqrt{3}m$
• B. 40m
• C. $20\sqrt{3}m$
• D. $40\sqrt{3}m$

Answer 1

The correct option is C $20\sqrt{3}m$

$h=5m,u=20m{s}^{-1},g=10m{s}^{-2}$

$h=\frac{u^{2}si{n}^2\theta }{2g}\Rightarrow sin\theta =\frac{\sqrt{2gh}}{u}=\frac{\sqrt{2\left(10\right)\left(5\right)}}{20}=0.5m$

$\Rightarrow \theta ={30}^{\circ }$

$\therefore R=\frac{u^{2}sin2\theta }{g}=20\sqrt{3}m$