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If r=a cost i +a sint j+at tan ak,then find values of |(dr/dt)*(d²r/dt²)| and(dr/dt)*(d²r/dt²)*(d^3r/dt^3).

If r=a cost i +a sint j+at tan ak,then
find values of |(dr/dt)*(d²r/dt²)|
and(dr/dt)*(d²r/dt²)*(d^3r/dt^3).

Grade:

4 Answers

vikas askiitian expert
509 Points
10 years ago

r = acost i +asint j +at(tanak) k..................1

 

dr/dt =ad/dt(cost) i  + ad/dt (sint)j+ (atana)d/dt(t) k

 

dr/dt =-asint +acost +atana k ...................2

 

d2r/dt2 = -acost i+ -asint j + 0 k            ...............3

 

d3r/dt3 = asint i -acost j                       ...............4

 

now use these equations and get ur ans ...

 

 

 

Dileep model
14 Points
14 days ago
askiitians.com
    0
 Forum Vectors Vectors problems
If r=a cost i +a sint j+at tan ak,then
find values of |(dr/dt)*(d²r/dt²)|
and(dr/dt)*(d²r/dt²)*(d^3r/dt^3).
 
PRADEEP KUMAR, 10 years ago
Grade:
 1 Answers
vikas askiitian expert 
 509 Points
10 years ago
r = acost i +asint j +at(tanak) k..................1
 
 
 
dr/dt =ad/dt(cost) i + ad/dt (sint)j+ (atana)d/dt(t) k
 
 
 
dr/dt =-asint +acost +atana k ...................2
 
 
 
d2r/dt2 = -acost i+ -asint j + 0 k ...............3
 
 
 
d3r/dt3 = asint i -acost j ...............4
Dileep model
14 Points
14 days ago
If r=a cost i +a sint j+at tan ak,then
find values of |(dr/dt)*(d²r/dt²)|
and(dr/dt)*(d²r/dt²)*(d^3r/dt^3).
Vaibhavi Gupta
13 Points
12 days ago
given r= acosti+asintj+attanak
dr/dt= -asinti+acostj+atanak
d^2r/dt^2= -acosti-asintj+0k
• |(dr/dt) x (d^2r/dt^2)|=| (a^2sint tana)i-(a^2cost tana)j+(a^2)k|
 |(dr/dt) x (d^2r/dt^2)|= a^2seca
• d^3r/dt^3 = asinti-acostj+0k
 (dr/dt) *(d^2r/dt^2) *(d^3r/dt^3) = -(asinti+acostj+atanak) *(-acosti-asintj) *(asinti-acostj) 

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