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Physics-

General

Easy

Question

A ball rolls of the top of stair-way with a horizontal velocity of magnitude $1.8 blank m s to the power of negative 1 end exponent.$ The steps are 0.20 m high and 0.20 m wide. Which step will the ball hit first?

First
Second
Third
Fourth

The correct answer is: Fourth

Given, $x equals 0.20 blank m comma blank y equals 0.20 blank m comma blank u equals 1.8 m s to the power of negative 1 end exponent$
Let the ball strike the $n$ th step of stairs,
$V e r t i c a l blank d i s t a n c e blank t r a v e l l e d$
$equals n y equals n cross times 0.20 equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent$
$H o r i z o n t a l blank d i s t a n c e blank t r a v e l l e d comma blank n x equals u t$
$o r blank t equals fraction numerator n x over denominator u end fraction$
$therefore n y equals fraction numerator 1 over denominator 2 end fraction g cross times fraction numerator n to the power of 2 end exponent x to the power of 2 end exponent over denominator u to the power of 2 end exponent end fraction$
$o r blank n equals fraction numerator 2 u to the power of 2 end exponent over denominator g end fraction fraction numerator y over denominator x to the power of 2 end exponent end fraction equals fraction numerator 2 cross times open parentheses 1.8 close parentheses to the power of 2 end exponent cross times 0.20 over denominator 9.8 cross times open parentheses 0.20 close parentheses to the power of 2 end exponent end fraction$
$equals 3.3 equals 4$

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