Brain Groomer

10/29/2024

09/13/2019

Question:
An object was sent straight up with an initial velocity "v". Suppose the frictional force can not be ignored and also assume that the deceleration due to friction is "a"

which time is greater:
1) time to go up, or
2) time taken to come down

Solution:
It will take longer to come down:

Details:
Assumption: the deceleration due to friction is constant
Important: Friction will act always against motion.

Upward motion:
Initial velocity = v
Final velocity = 0
acceleration = -(g + a)
both friction and gravitation force act down, opposite to direction of motion

Time take t_up = (o - v) / (-(g+a)) = v / (g + a)

Height reached = h = v * t_up + (1/2) (-(g+a)) (t_up)^2
h = v^2 / (g+a) - (1/2) v^2/ (g+a)
= v^2 / (g+a)

Downward motion:
Initial velocity = 0
acceleration = -(g -a)
displacement initial = h
displacement final = 0
While gravitational force is downwards while frictional force will be against motion

let the time to reach back is t_down

0 = h + 0 * t_down + (1/2) (-(g-a)) (t_down)^2
(t_down)^2 = -h / { (1/2) (-(g-a))} substituting for h we get
(t_down)^2 = (v^2) / ((g+a) * (g-a))

t_down = v / square root ((g+a) * (g-a))

t_up = v / (g+a)

==> t_down > t_up

Numerator is same for both t_down has less denominator ==> higher value

12/09/2018

Congratulations to Speech and Debate Winners
Anish Kristipati - Congressional Debate
Ananya Seelam - Lincoln Douglas Debate
BG scholars from Enloe High School.

12/31/2017

Congratulations to Ms. Labannya (faculty at Brain Groomer) for standing first in her class at North Carolina State University. We wish her further success!!!
Venkat

11/24/2017

Physics Lab was conducted o promote students into STEM field.

07/12/2017

Congratulations to Dr. Sundar. You have coached the following students to reach high level of achievement in various competitions:
Highlights of 2016-2017
1 CTY Grand Ceremony (S**T) Neha
2 MathCounts School Team Sri
3 Duke TIP State Award Ceremony Neha
4 Duke TIP Grand Ceremony Neha
5 CTY Top Honors Ceremony Neha
6 CTY Grand Ceremony Neha
7 MathCounts School Team Sri
8 AMC 8 Distinguished Honor Roll Sri
9 Duke TIP State Award Ceremony Anish
10 CTY Top Honors Ceremony Anish
11 CTY Grand Ceremony Anish
12 AMC 10 Achievement Roll Sri
13 Pratham Level 3 3rd Naveen
14 Pratham Level 3 5th Aakash
15 Pratham Level 3 6th Yashas
16 Pratham Level 2 1st Siddharth
17 NSF Math Bee Level 2 9th Siddharth
18 NSF Sr Geo Bee 6th Aakash
19 CTY Top Honors Ceremony Naveen
20 CTY Grand Ceremony Naveen
21 NSF Math Bee Level 3 National List Sri
22 NSF Sr Geo Bee National List Aakash
23 Math Kangaroo National Ranking Siddharth
24 CTY Top Honors Ceremony Gautham
25 CTY Grand Ceremony Gautham
26 CTY Top Honors Ceremony Yashas, Umesh, Srinithi, Bharath, Aakash
27 CTY Grand Ceremony Yashas

Great Job!!!

09/06/2016

http://www.evite.com/services/events/00E3MNASKVWREU4WWEPGOLUKELUPYA/export/facebook/1473192731.33/

You're invited to Information session/ Volunteering opportunity - Click here to RSVP

07/12/2016

Calculus: Application of derivatives. Plotting functions.
https://drive.google.com/open?id=0Bz63gILValc1YWxncFE3VzRaYmc

07/10/2016

Calculus Continuity and differentiability Problem

06/30/2016

Calculus: Significance of first and second derivative of functions.
https://drive.google.com/open?id=0Bz63gILValc1S1RlSkNFZzNWcjA

06/04/2016

04/27/2016

Problem:
An arithmetic series of positive integers has 8 terms and a sum of 2008. What is the smallest possible value of any member of series.

This problem is from Math count trainer. I think it will be a good one for CC2, CC3, SAT and ACT students. I will post the answer after sending this to BrainGroomer students.. regards

Venkat