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Physics-

General

Easy

Question

A ball rolls off the top of a stairway with horizontal velocity $v subscript 0 end subscript m s to the power of negative 1 end exponent$ . If the steps are $h$ metre high and $w$ metre wide, the ball will hit the edge of $n$ th step if

$n = \frac{2 h v_{0}}{g w^{2}}$
$n = \frac{2 h v_{0}^{2}}{g w}$
$n = \frac{h v_{0}^{2}}{g w^{2}}$
$n = \frac{2 h v_{0}^{2}}{g w^{2}}$

The correct answer is: $n equals fraction numerator 2 h v subscript 0 end subscript superscript 2 end superscript over denominator g w to the power of 2 end exponent end fraction$

For horizontal motion,
$n w equals v subscript 0 end subscript t blank o r blank t equals fraction numerator n w over denominator v subscript 0 end subscript end fraction$
For vertical motion, $n h equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent$
or $fraction numerator 1 over denominator 2 end fraction g open parentheses fraction numerator n to the power of 2 end exponent w to the power of 2 end exponent over denominator v subscript 0 end subscript superscript 2 end superscript end fraction close parentheses equals n h blank o r blank n equals fraction numerator 2 h v subscript 0 end subscript superscript 2 end superscript over denominator g w to the power of 2 end exponent end fraction$

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