A ball rolls off the top of a stariway with a horizontal velocity magnitude 150 cm/sec. The steps are 20 cm high and 20 cm wide . Which step will the ball hit first ?

Explanation

Let x be the horizontal distance measured from the foot of the edge of the step , the ball laves the top of stariway to the point it hit the `n^(th)` step .
`x = v_(0) t= 1.5 t" "……(i)`
where `v_(0)` is the initial horizontal speed. The height of the ball drops throuph is .
`y = nH = 0.2 n" "......(ii)`
Where n is number step and H =20 cm is the height speed. As the vertical component of initial velocity is zero , the vertical distance traversed in the same time t is .
`y = (1)/(2) "gt"^(2)" "......(iii)`
and `x = nw = 0.2 n " "...(iv)`
`x = y = 0.2n" "........(iv)` `rArr " " t= 0.3s`
`therefore 0.2n = 1.5 (0.3) rArr n = 2.25 m therefore n = 3`