A particle (A) is dropped from a height and another particle (B) is thrown in the horizontal direction with a

Question

A particle (A) is dropped from a height and another particle (B) is thrown in the horizontal direction with a speed of 5 m/sec from the same height. The correct statement is:

Accepted Answer

1.  **Independence of Motions:** The motion of an object can be resolved into independent horizontal ($x$) and vertical ($y$) components. The vertical motion is acted upon by gravity, while the horizontal motion (ignoring air resistance) has zero acceleration .
2.  **Vertical Motion Analysis:** Both particles start from the same height $h$. Particle A is dropped, so its initial vertical velocity $u_{yA} = 0$. Particle B is thrown horizontally, so its initial vertical velocity is also $u_{yB} = 0$ (its initial velocity is entirely horizontal) .
3.  **Time of Flight:** The time $t$ taken to reach the ground depends only on the vertical parameters: $h = u_y t + \frac{1}{2}gt^2$. Since $u_y = 0$ for both, $h = \frac{1}{2}gt^2$ implies $t = \sqrt{\frac{2h}{g}}$.
4.  **Conclusion:** Since $h$ and $g$ are the same for both particles, the time $t$ is the same. Therefore, they reach the ground simultaneously. (Note: Their final speeds will differ because Particle B has a horizontal velocity component, while Particle A does not).

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