A staircase contains three steps each 10 cm high and 20 cm wide. What should be the minimum horizontal velocity of a ball rolling of the uppermost plane so that it hits directly the lowermost plane.
Kinematics.png
For the ball to hit the lowermost plane directly with min. initial velocity, it would just need to pass through the very close proximity of point A (refer figure attached).
For horizontal motion upto point A, 0.4 = ut
For vertical motion upto point A, \(0.2=\frac {1}{2}gt^2\)
You can eliminate t and solve for u.
Staircase_Projectile_Motion.png
Consider this as a complete projectile of max ht. 30 cm...
for gettin max range and ht. the angle must be 45degree...
so h=30 cm..
using h=u^2*sin^2 alpha/2g
we get,
u as 20*root3....
horizontal component is U*sin alpha=20*root3/root2=10*root6