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A roller coaster car travels down the he...

A roller coaster car travels down the helical path at constant speed such that it's parametric coordinates varies as `x = x sin(kt), y = c cos(kt), z = h - bt` where c, h, k and b are constants, then the megnitude of it's acceleration is :

A

`0`

B

`ck^(2)`

C

`(c^(2)k^(2))/(h)`

D

`bk^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
A roller ………..
`x = c sin kt a_(x)= (d^(2)x)/(dt^(2))= -ck^(2)sin kt`
`y = c cos kt a_(y) = (d^(2)y)/(dt^(2))= -ck^(2)cos kt`
`z= h - bt a_(z) = 0`
`a = sq1rt(a_(n)^(2)+a_(y)^(2)+a_(z)^(2))`
`a = ck^(2)`
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