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A marble is rolled so that it is projected horizontally off the top landing of a...

A marble is rolled so that it is projected horizontally off the top landing of a staircase. The initial speed of the marble is 3.1 m/s. Each step is 0.19 m high and 0.28 m wide. Which step does the marble strike first?

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Answer #1

for vertical motion, lets use Sy= ut + 0.5gt^2
for horizpntal motion, Sx = 3.1t
in these 2 cases, time is the same since marble touch the stair at same time ,

do sustitution we got ..... Sy= (0)( Sx/3.1) + 0.5(9.81)( Sx/3.1)^2

Sy= 0.5104 Sx^2

but Sy = 0.19n Sx = 0.28n , n is numbers of ladder....

So 0.19n = 0.5104 ( 0.28n)^2
solving equation, found out n = 0 or 4.748...

since 4.748 means still around 4th stairs....

the ball 1st touch on the 4th stairs

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