Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 11-science Answered

v vector = 2icap + 3jcap ; a vector = icap + jcap. find rate of change of direction at an instant?

Asked by kapilkulhari | 24 May, 2019, 08:27: PM
Expert Answer
begin mathsize 14px style v with rightwards arrow on top space equals space 2 i with hat on top space plus space 3 j with hat on top space space space semicolon space space space space a with rightwards arrow on top equals i with hat on top space plus space j with hat on top space end style
It is assumed that vector-v is initial velocity and vector-a is acceleration vector .
Also it is assumed that it is required to find the rate of change of direction of instantaneous velocity vector V at any instant t
 
Hence velocity V at any instant t is  begin mathsize 14px style V with rightwards arrow on top space equals space v with rightwards arrow on top space plus space a with rightwards arrow on top t space space equals space open parentheses space 2 i with hat on top space plus space 3 j with hat on top space close parentheses space plus space open parentheses space i with hat on top space plus space j with hat on top space close parentheses t space equals space open parentheses 2 plus t close parentheses i with hat on top space plus space open parentheses 3 plus t close parentheses j with hat on top space end style  
if θ is the angle made by the vector with x-axis is considered as direction  ,
then direction of vector in terms of tangent of the angle θ is given by
 
begin mathsize 14px style tan theta space equals space fraction numerator 3 space plus space t over denominator 2 space plus space t end fraction
B y space d i f f e r e n t i a t i n g comma space space fraction numerator d theta over denominator d t end fraction space equals space fraction numerator 1 over denominator s e c squared theta end fraction cross times fraction numerator open parentheses 2 plus t close parentheses space minus space open parentheses 3 plus t close parentheses over denominator open parentheses 2 plus t close parentheses squared end fraction space equals space fraction numerator open parentheses 2 plus t close parentheses squared over denominator open parentheses 2 plus t close parentheses squared space plus space open parentheses 3 plus t close parentheses squared end fraction cross times fraction numerator negative 1 over denominator open parentheses 2 plus t close parentheses squared end fraction
fraction numerator d theta over denominator d t end fraction space equals space fraction numerator negative 1 over denominator open parentheses 2 plus t close parentheses squared space plus space open parentheses 3 plus t close parentheses squared end fraction end style
Answered by Thiyagarajan K | 26 May, 2019, 08:49: AM
CBSE 11-science - Physics
Asked by ankurgoyal616 | 27 Sep, 2022, 03:07: PM
ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by mahekacharya87 | 20 Sep, 2022, 10:41: AM
ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by rk274268 | 05 Aug, 2022, 01:19: PM
ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by halderishan008 | 30 Jul, 2022, 07:28: PM
ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by Kattaithihaas | 24 Jul, 2022, 01:23: PM
ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by ukalyadab | 18 Jul, 2022, 11:52: AM
ANSWERED BY EXPERT
CBSE 11-science - Physics
Asked by madhavrao135 | 13 Jul, 2022, 07:33: PM
ANSWERED BY EXPERT

Start your hassle free Education Franchisee and grow your business!

Know more
×