Question

A staircase contains three steps each 10 cm high and 20 cm wide figure. What should be the minimum horizontal velocity of a ball rilling off the uppermost plane so as to hit directly the lowest plane?

Answer 1

Step 1,

At minimum velocity, the ball will move just touching point E and reaches the ground.

A is the origin of the coordinate system.

The ball needs to cover a minimum of 40 cm to cross next to two steps along the horizontal axis and a minimum of 20 cm in the vertically downward direction.

If u is the minimum speed,

Then we have, x = 40, y = -20 cm, θ=00

Step 2,

We can use equation of trajectory because it is valid for all type of projectile motion.

The equation of the trajectory of a projectile is given by, $y=x\tan \theta -\raisebox{1ex}{$g{x}^2$}\!\left/ \!\raisebox{-1ex}{$2u^2{\cos }^2\theta $}\right.$

Where g = 10 m/s2=1000 cm/s2

⇒−20=0−(1000)×(40)²/(1)2u²

⇒20=1600000/2u²

u2=1600000/40=40000

⇒u=√40000

⇒u=200cm/s=2m/s

∴ The minimum horizontall velocity is 2 m/s.