The ceiling of a long hall is $25 ext{ m}$ high. What is the maximum horizontal distance that a bal

Question

The ceiling of a long hall is $25	ext{ m}$ high. What is the maximum horizontal distance that a ball thrown with a speed of $40	ext{ m/s}$ can go without hitting the ceiling of the hall? (Take $g = 9.8	ext{ m/s}^2$)

Professor PC Thomas Classes · Answer

Max height $H = \frac{u^2\sin^2	heta}{2g} \le 25 \Rightarrow \frac{1600\sin^2	heta}{19.6} = 25 \Rightarrow \sin^2	heta = \frac{490}{1600} \Rightarrow \sin	heta = \frac{7}{\sqrt{160}}$, so $\cos	heta = \frac{\sqrt{111}}{\sqrt{160}}$. Range $R = \frac{2u^2\sin	heta\cos	heta}{g} = \frac{2(1600)}{9.8} \left(\frac{7}{\sqrt{160}}ight) \left(\frac{\sqrt{111}}{\sqrt{160}}ight) \approx 150.5	ext{ m}$.