A particle (a) is dropped from a height and another particle (b) is projected in the horizontal direction…

A particle (a) is dropped from a height and another particle (b) is projected in the horizontal direction with a speed of $5 \mathrm{~ms}^{-1}$ from the same height, then the correct statement is:
  1. particle (a) will reach at the ground first with respect to particle (b)
  2. particle (b) will reach at the ground first with respect to particle (a)
  3. both particle will reach at the ground simultaneously
  4. both particles will reach at the ground with the same speed

Solution


For particle A
$\begin{aligned}
& h=\frac{1}{2} g t^2 \\
& t_{\mathrm{A}}=\sqrt{\frac{2 h}{g}}
\end{aligned}$
For particle B. In vertical direction
Using $\mathrm{S}=u t+\frac{1}{2}+a t^2$
$\Rightarrow h=\frac{1}{2} g+t_n^2 \Rightarrow t_{\mathrm{B}}=\sqrt{\frac{2 h}{g}}$

Asked in: NEET 2002

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