Question

What is the maximum range that a ball thrown with a speed of 40 ms^-1 can cover without hitting the 25 m high ceiling of a long hall?

• A. 150.5 m
• B. 100.25 m
• C. 110.3 m
• D. 200.5 m

Answer 1

Answer: (A)

150.5 m

Answer 2

Using H = u² sin²α/2g

and R = $\frac{2u^{2}\sin\alpha\cos\alpha}{g}$

we get R² = $\frac{4u^{4}}{g^{2}}$sin²α cos²α

Eliminating α, we get

R² = $\frac{4u^{2}}{g}\frac{2gH}{u^{2}}\left( 1 - \frac{2gH}{u^{2}} \right)$

= $\frac{8H}{g}\left( u^{2} - 2gH \right)$

or R = $\left\lbrack \frac{8H}{g}\left( u^{2} - 2gH \right) \right\rbrack^{1/2}$

= $\left\lbrack \frac{8 \times 25}{9.8}\left( 40^{2} - 2 \times 9.8 \times 25 \right) \right\rbrack^{1/2}$