Question

42. A staircase contains three steps each 10 cm high and
20 cm wide (figure 3-E9). What should be the minimum
horizontal velocity of a ball rolling off the uppermost
plane so as to hit directly the lowest plane ?​

Answer 1

Answer:

h= height

w= width of each step

O= uppermost plane

A= lowermost plane

Consider the ball roll from the upmost plane O with horizontal velocity v here the vertical velocity in the y direction will be 0

X=vt

t=

v

x

...................(1)

The horizontal range of the ball lies between 2wand3w

Horizontal range x of the ball will be greater than 2w.

h=10cm=0.10m

w=20cm=0.20m

i.e,x≥2w

x≥3×0.20

x≥0.40m

The ball travels form plane O to plan A=2h

equation of motion, s=ut+(

2

1

)gt

2

u=0 for vertical motion

2h=ut+(

2

1

)gt

2

t=

g

4h

......................(2)

form (1)and (2)

v

x

=

g

4h

x=

v

g

4h

we know x≥0.40m

v

g

4h

≥0.40m

0.20v≥0.40

v≥2m/s

I hope that it is helpful to you.