When the balls collide, they are moving in oppowebsite direction and the rate of A is twice the speed of B. At what fractivity of the height did the collision occur?

Now I have resolved this question a little in different ways. I did not arrive at the appropriate answer, so I have to understand what I have to fix.

You are watching: A ball is dropped from the top of a building

Let the building be of height H and let the balls collide at h and time t

Distance took a trip by A$$H-h=frac 12 gt^2$$So $$t^2=frac 2g (H-h)$$And distance spanned by B is

$$h=ut - frac 12 gt^2$$Subsisting the value of t$$h=usqrt frac2(H-h)g - (H-h)$$Squaring after doing appropriate simplification $$H^2=frac2u^2(H-h)g$$I don’t recognize how to continue additionally. Please assist.


kinematics
Share
Cite
Follow
asked Sep 6 "19 at 16:44
*

Aditya Aditya
5,92811 gold badge1111 silver badges3939 bronze badges
$endgroup$
Add a comment |

3 Answers 3


Active Oldest Votes
1
$egingroup$
The distances traveled by the two balls

$$h =ut - frac 12 gt^2$$$$H - h = frac 12 gt^2$$

Take their ratio

$$ frac hH-h = frac2ugt -1 ag1$$

Let $u_a$ and $u_b$ be the velocities at collision, then $gt$ is pertained to them via

$$gt = u-u_b = u_a ag2 $$

And, at collision,

$$u_a= 2u_b ag3$$

From (2) and also (3), we acquire $u=3u_b$, which leads to

$$gt = u-u_b = frac23 u$$

Plug over $gt$ into (1) to get

$$ frac hH-h = frac 21$$

Therefore, they collide at

$$h=frac23 H$$.


Share
Cite
Follow
edited Sep 7 "19 at 6:08
answered Sep 6 "19 at 17:32
*

QuantoQuanto
60.3k55 gold badges4141 silver badges8787 bronze badges
$endgroup$
2
Add a comment |
2
$egingroup$
At first A is dropped at remainder , after time t it"s velocity is $2v=gt$ , or $v=5t$. and also let B is thrown by Initial velocity u . $u-gt=v$ or $u=15t$ . currently use $s= ut+1 over 2gt^2$.

$$S_A=0(t)+5t^2=5t^2$$$$S_B=15t(t)-5t^2=10t^2$$$$S_A over S_B=1 over 2 $$&$$S_A+S_B=H$$>Ratio is $$fracS_BS_A+S_B=2 over 3$$


Share
Cite
Follow
edited Sep 6 "19 at 17:22
answered Sep 6 "19 at 16:58
*

RishiRishi
92233 silver badges1212 bronze badges
$endgroup$
5
Add a comment |
0
$egingroup$
The closing rate will certainly reprimary consistent and is equal to the initial rate of $B (Vib)$ so $Va + Vb = Vib$.

When they collide, $Va = 2Vb$

We can check out that $Vib = 3Vb$ at the collision.

So: The rate of A goes from $0$ to $2Vb$ and also the rate of B goes from $3Vb$ to $Vb$

Distance is average velocity times time.

$s(Va) = Vbcdot t$

$s(Vb) = 2Vbcdot t$

$B$ travels twice as much as $A$ so the fraction of the height the collision occurs is $frac23$.

I think tright here is one more solution wbelow $B$ reverses direction and starts to fall and is eventually recorded by $A$.

Here $Va - Vb = Vib$

And $Vib = Vb$ at the collision.

In this scenario, the speed of $A$ goes from $0$ to $2Vb$ and also the speed of $B$ goes from $Vb$ to $-Vb$.

$s(Va) = Vbcdot t$

$s(Vb) = 0cdot t$

In this scenario the height the collision occurs is $0$.


Share
Cite
Follow
edited Sep 6 "19 at 18:12
answered Sep 6 "19 at 17:18
*

Phil HPhil H
5,41122 gold badges66 silver badges1414 bronze badges
$endgroup$
Add a comment |

Your Answer


Thanks for contributing a solution to soimg.orgematics Stack Exchange!

Please be certain to answer the question. Provide details and share your research!

But avoid

Asking for aid, clarification, or responding to various other answers.Making statements based on opinion; earlier them up via recommendations or personal endure.

Use soimg.orgJax to format equations. soimg.orgJax reference.

To learn more, see our tips on composing good answers.

See more: 17 Reasons Why Does My Dog Stare At The Ceiling And Sometimes Barks At It


Draft saved
Draft discarded

Sign up or log in


Sign up utilizing Google
Sign up utilizing Facebook
Sign up using Email and Password
Submit

Blog post as a guest


Name
Email Required, but never shown


Blog post as a guest


Name
Email

Required, but never before shown


Blog post Your Answer Discard

By clicking “Article Your Answer”, you agree to our terms of company, privacy plan and cookie plan


Not the answer you're looking for? Browse various other questions tagged kinematics or ask your very own question.


Featured on Meta
*

14 votes · comment · stats
Related
3
A ball is dropped on the ground and bounces earlier to a height rather less than the original height. Which of the curves depicts its motion effectively
Hot Netoccupational Questions even more hot inquiries

Question feed
Subscribe to RSS
Inquiry feed To subscribe to this RSS feed, copy and also paste this URL right into your RSS reader.


soimg.orgematics
Company type of
Stack Exreadjust Network
website design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. rev2021.9.10.40187


soimg.orgematics Stack Exadjust works ideal with JavaScript allowed
*

Your privacy

By clicking “Accept all cookies”, you agree Stack Exadjust can keep cookies on your device and discshed information in accordance through our Cookie Policy.