Question

Two particles are projected in air with speed $u$ at angles ${\theta }_1$ and ${\theta }_2$ (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then which one of the following is correct?
where $T_1$ and $T_2$ are the time of flight.

• A. ${\theta }_1>{\theta }_2$
• B. ${\theta }_1={\theta }_2$
• C. $T_1<T_2$
• D. $T_1=T_2$

Answer 1

Answer: (A)

Height,
$H=\frac{u^{2}si{n}^2\theta }{2g}$
For the same speed,
$H\propto si{n}^2\theta$
$\because H_1>H_2$ (Given)
$\therefore si{n}^2{\theta }_1>si{n}^2{\theta }_2$ or
${\theta }_1>{\theta }_2$
Time of flight,
$T=\frac{2usin\theta }{g}$
For the same speed,
$T\propto sin\theta$
$\because {\theta }_1>{\theta }_2$ or
$sin{\theta }_1>sin{\theta }_2$
$\Rightarrow T_1>T_2$