Question

A ball rolls off the top of a star way with a horizontal velocity $10\sqrt{10}$. If the steps are 0.25 m high and 5 m wide then the ball will hit the edge of the $n^{th}$ step where $n$ is

• A. 6
• B. 2
• C. 4
• D. 3

Answer 1

The correct option is B 2

We know horizontal distance covered by the ball$=nb$ where n=number of steps and b=breadth of the step.

So $v=\frac{nb}{t}$

$t=\frac{5n}{10\sqrt{10}}$

And vertical distance covered by the ball $=nh$ where h= height of the step.

Now from equation of motion we get

$s=ut+\frac{1}{2}g{t}^2$ here s=nh and u= initial velocity = 0 m/s

$0.25n=\frac{1}{2}\times 10\times (\frac{5n}{10\sqrt{10}}{)}^2$

$n=2$