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The position vector of a particle moving...

The position vector of a particle moving in x-y plane is given by `vec(r)=(t^(2)-4)hat(i)+(t-4)hat(j)`. Find
(a) Equation of trajectory of the particle
(b)Time when it crosses x-axis and y-axis

Text Solution

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The correct Answer is:
(a)`y^(2)+8y+12=x` ; (b) crosses x axis when `t =4sec`. , crosses y axis when `t=+2`sec.
(a)`x=t^(2)-4=(t+2)(t-2)`
`y=t-4=(t-2)-2`
`(y+2)=(t-2)`
`(y+6)=(t+2)`
`x=(y+2)=(y+6)`
`x=y^(2)+8y+12`
(b) When crosses x axis , at this time `y=0,rArrt-4=0rArrt=4 sec`
When crosses y axis, ` X=0, rArr T^(2)-4=0 rArr t=2 sec`
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