Kinematics

Two bodies begin a free fall from the same height, $t$ seconds apart. How long after the first body begins to fall will the both bodies be $x$ meters apart?

The particles never reach the ground and ignore air resistance.

#Mechanics

Easy Math Editor

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Comments

Equation for displacement of first body is $s_1=\dfrac 1 2 gy^2$ where $y$ is the time(in sec).

Equation for displacement of second body is $s_2=\dfrac 1 2 gz^2$ where $z$ is the time(in sec).

We have $y-z=t$ or $z=y-t$ and $s_1-s_2=x$ .

We can rewrite this as $\dfrac 1 2 gy^2-\dfrac 1 2 gz^2=x$ or $\dfrac 1 2 gy^2-\dfrac 1 2 g(y-t)^2=x$ .

Now simplifying we have $\dfrac {2x} g =(2y-t)(t)$ .

A Former Brilliant Member - 5 years, 1 month ago

Same :)

A Former Brilliant Member - 5 years, 1 month ago

Same here too

Krishna Karthik - 2 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$