Question

A ball rolls off the top of the stairway with a horizontal velocity of magnitude \[1.8m/s\]. The steps are \[0.20m\;\] high and \[0.20m\;\] wide. Which step will the ball hit first?
$\left( A \right)$ First
$\left( B \right)$ Second
$\left( C \right)$ Third
$\left( D \right)$ Fourth

Answer 1

Hint: When an object is made to fall from a higher level the potential energy converts it into kinetic energy of the motion. The energy possessed by the body due its motion is termed as Kinetic energy. Apply the formula to find a place where horizontal and vertical distance becomes equal. Then we can obtain the distance travelled by the ball.

Formula used:
$t = \dfrac{{2u}}{g}$
Where $t$ is the time, $u$ is the initial velocity

Complete step by step answer:
The energy stored as a result of deforming an elastic body is termed as Elastic potential. The energy will be retained until the force is removed and the springs reach its original shape. Potential energy is the energy stored due to its location or configuration.
The energy possessed by a body due its motion is termed as Kinetic energy. It is determined that the body can do work against a restraining force action on the body before the body comes to rest.
Ball will roll off the top of stairway with horizontal velocity $u = 1.8m/s$.
Here the staircase has the same width and height hence, we have to find a place where horizontal and vertical distance becomes equal.
$\Rightarrow$ $ut = \dfrac{1}{2}g{t^2}$
$\Rightarrow$ $t = \dfrac{{2u}}{g} = \dfrac{{2 \times 1.8}}{{10}} = 0.36s$
Horizontal distance covered
$\Rightarrow$ $ut = 1.8 \times 0.36 = 0.648m$
Then the ball will reach in $\dfrac{{0.648}}{{0.2}} = 3.24$.
Hence the ball will hit on the fourth step.

Option D is the correct option.

Note: Potential energy is the stored energy inside the body, when the body is deformed. When the body retains its original state, the potential energy stored in the body will get converted to kinetic energy. Potential energy is the energy stored due to its location or configuration. The energy possessed by a body due its motion is termed as Kinetic energy.