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a stair case contains 3 steps each of10 cm high and 20 cm wide .whatshould be minimum horizontal velocity of a ball rolling off the uppermost plane so as to hit directlythe lowest plane

a stair case contains 3 steps each of10 cm high and 20 cm wide .whatshould be minimum horizontal velocity of a ball rolling off the uppermost plane so as to hit directlythe lowest plane
 

Grade:12

3 Answers

Arun
25750 Points
4 years ago
hit directly the lowest plane the ball has to cross the point B.
From A to B, the  ball has to travel to horizontal distance equal 40cm =40m
and vertical distance of 20cm=0.2m.
 
Let the time taken to reach point be t.u=0 m/s
h=0.2m
from the equation, h=ut+1/2gt²
 
we get
0.2=0+1/2 x9.8 t²
t²=0.4/9.8
t²=0.04
t=0.2
Let v be the horizontal velocity of ball than the horizontal distance travelled by the ball=0.2v
in order to clear the point B it must be equal to 0.40.
2v=0.4
v=2m/s
∴So minimum velocity required to to hit the lowest floor  is 2 m/s.
Vikas TU
14149 Points
4 years ago
Dear student 
in a friction-less rolling of the ball, the number, height and width of the steps have no effect on the horizontal velocity.
Falling off the edge of a higher step to a lower one, the ball gains some vertical velocity due to gravitational acceleration, but the vertical momentum gained is absorbed on impact with the lower step. So the ball maintains its original initial horizontal velocity.
If rolling friction is present, one should expect some decrease from the initial velocity.
Hope this helps 
Good Luck
aswanth nayak
100 Points
4 years ago
Dear Student,
 
Let the time taken to reach point be t.u=0 m/s
h=0.2m
from the equation, h=ut+1/2gt²
we get
0.2=0+1/2 x9.8 t²
t²=0.4/9.8
t²=0.04
t=0.2
Let v be the horizontal velocity of ball than the horizontal distance travelled by the ball=0.2v
in order to clear the point B it must be equal to 0.40.
2v=0.4
v=2m/s
∴So minimum velocity required to to hit the lowest floor  is 2 m/s. 
 
 
Regards

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