Question

please solve this question I'll mark u as BRAINLIEST no spamming​

Answer 1

${\bold{\underline{Heya \:Mate!!}}}$

Here's the Answer ❗

${\bold{Question }}$ → A ball a dropped from the top of a building and at the same time an identical ball B is thrown vertically upward from the ground . When the balls collide , the speed of A is twice that of B. At what fraction of the height of the building did the collision occur?

Answer .

Firstly for ball A we have ,

Initial Velocity u = 0

Distance s = ( 1 - x )h

Using the second equation of motion

$s = ut + \frac{1}{2} at {}^{2}$

Put the values here ,

$= > (1 - x)h = \frac{1}{2} gt {}^{2}$

From here time t

$t = \sqrt{2(1 - x) \frac{h}{g} }$

Now by using the first equation of motion

v = u + at

$v = g \sqrt{2(1 - x) \frac{h}{g} } ..............(1)$

[ as here u is zero. Instead of t putting the value we derived above ]

_________________

Now for Ball B ,

Distance travelled s = xh

Again following the steps as done for A ,

$xh = u \sqrt{2(1 - x) \frac{h}{g} } - \frac{1}{2} g(2(1 - x) \frac{h}{g} )$

[ Here again instead of t we have put the value derived as time for both is same. Now as the ball is thrown against gravity , g will be negative ]

From this equation We derive the value of u

$= > u = \sqrt{ \frac{gh}{2(1 - x)} }$

Now here v = u - gt

$= > v = \sqrt{ \frac{gh}{2(1 - x)} } - \sqrt{2g(1 - x)h} ...........(2)$

Va = 2 ( Vb)

As per the question we have

$\sqrt{2g(1 - x) h } = 2\times \sqrt{ \frac{gh}{2(1 - x)} } - 2 \sqrt{2g(1 - x) h} \\ \\ = >3 \sqrt{} 2g(1 - x)h = 2 \sqrt{ \frac{gh}{2(1 - x)} } \\ = > 9(1 - x) = \frac{1}{1 - x} \\ \\ = > 9(1 - x) {}^{2} = 1 \\ = > (1 - x) {}^{2} = \frac{1}{9}$

•°• ( 1 - x ) = ±⅓

So we have ,

${ \bold{{taking \: positive\: value \:}}} = > \: \\ = > 1 - x = \frac{1}{3} \\ = > x = 1 - \frac{1}{3} = \frac{2}{3}$

•°• ${\underline{\underline{Answer}}}$ → $\frac{2}{3}$

${\boxed{\bold{Hope\:Helps!!}}}$

Answer 2

Answer:

please refer to the attachment

I hope it would help you

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anyways,

u just study well.

practice more.

forget less.

think most.

THANK YOU ‼️‼️✴️✴️✴️✴️