Question

For a projectile, the ratio of maximum height reached to the square of the time of flight is $(g=10m{s}^{-2})$

• A. $5:4$
• B. $5:2$
• C. $5:1$
• D. $10:1$

Answer 1

The correct option is A $5:4$

$H_{max}=\frac{u^2{\sin }^2\theta }{2g}$

$T=\frac{2u\sin \theta }{g}$

$\frac{H_{max}}{T^2}=\frac{\left(u^2{\sin }^2\theta \right)}{2g}\frac{g^2}{4u^2{\sin }^2\theta }=\frac{g}{8}=\frac{10}{8}=\frac{5}{4}$