Question

A particle is placed at the point A of a frictionless track ABC as shown in figure.It is pushed slightly towards right.Its speed when it reaches the point B is (g=10 m/s^2)

Answer 1

$\displaystyle\large\boxed {\sf {v=\sqrt{10}\ m\ s^{-1}}}$

To find the velocity of the particle at B we have to consider vertical motion.

Even the particle is moved rightwards from A, its initial vertical velocity is zero, i.e.,

• $\displaystyle\sf {u_y=0}$

When the particle reaches B it's vertical displacement is,

• $\displaystyle\sf {s_y=(1.0-0.5)\ m}$

• $\displaystyle\sf {s_y=0.5\ m}$

The vertical acceleration,

• $\displaystyle\sf {a_y=g=10\ m\ s^{-2}}$

Then, by the third kinematic equation,

$\displaystyle\longrightarrow\sf {v_y=\sqrt{(u_y)^2+2a_ys_y}\ m\ s^{-1}}$

$\displaystyle\longrightarrow\sf {v_y=\sqrt{0^2+2\cdot10\cdot0.5}\ m\ s^{-1}}$

$\displaystyle\longrightarrow\sf {\underline {\underline {v_y=\sqrt{10}\ m\ s^{-1}}}}$