Question

A particle is given velocity
$4m/s$ along the $y$-axis subjected to constant acceleration $10m/s^2$ at ${53}^{\circ }$ with the $x$-axis. The displacement of the particle along the coordinate axes after $3s$ is $(x,y)m$. Find $(y-x)$.

Answer 1

Draw a labelled diagram.


Find the displacement of the particle.
For $x$: (constant acceleration)
Therefore, we use
$x=u_{x}t+\frac{1}{2}{a}_x{t}^2$
$x=0+\frac{1}{2}\times 6\times 3^2=27m$
For $y$:(constant acceleration)
Therefore, we use
$y=u_{y}t+\frac{1}{2}{a}_y{t}^2$
$y=4\times 3+\frac{1}{2}\times 8\times 3^2$
$y=12+36=48m$
Coordinates of particle after $3s(27m,48m)$
Therefore $y-x=48-27=21$
Final Answer: (21)