Question

At time $t=0$, a particle of mass $3kg$ was at a point (in X-Y plane) with position vector $(9\hat{i}+3\hat{j})$ m and its velocity was $(3\hat{i}+4\hat{j}+4\hat{k})$ m/s. Now a force $(3\hat{i}+12\hat{j}-24\hat{k})$ N operates upon it continuously. Find the Y component (in m/s) of its velocity when it hits the X-Y plane again.

Answer 1

Initially $z=0$
Given, $u_z=4$
$a_z=\frac{-24}{3}=-8m/s^2$
Let z-co-ordinate of the particle becomes zero after time t.
$z=u_{z}t+\frac{1}{2}a{t}^2=4t-\frac{1}{2}\times \frac{24}{3}\times t^2=4t(1-t)=0$
$\Rightarrow t=1$
$v_y=u_y+a_{y}t=4+\frac{12}{3}\times 1=4+4=8m/s$