1. Tardigrade
  2. Question
  3. Physics
  4. A particle starts from origin at t=0 with a velocity 5 hati m / s and moves in x-y plane under action of a force which produces a constant acceleration of (3 hati+2 hatj) m / s 2 The y -coordinate of the particle, when its x -coordinate is 84 m is

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Q. A particle starts from origin at $t=0$ with a velocity $5 \hat{i} \,m / s$ and moves in $x-y$ plane under action of a force which produces a constant acceleration of $(3 \hat{i}+2 \hat{j})\, m / s ^{2}$ The $y$ -coordinate of the particle, when its $x$ -coordinate is $84 \,m$ is

Motion in a Plane

Solution:

The position of the particle is given by
$s=\left(u_{x}+u_{y}\right)+\frac{1}{2}\left(a_{x}+a_{y}\right) t^{2}$
Hence, $x=5 t+1.5 t^{2}, y=1 \,t^{2}$
Given $x(t)=84 \,m , y=$ ?
$5 t+1.5 t^{2}=84$
$\Rightarrow t=6 \,s$
At $t=6 \,s , y=6^{2}=36 \,m$