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

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