Kinematics problem, ball drop.

[AlchemistK]

Homework Statement

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

Homework Equations

s= u*t + 1/2 a*t^2

The Attempt at a Solution

In the vertical motion,
s= u*t + 1/2 a*t^2
=> 0.3 = 0 + 1/2 * 10 * t^2
=>t= \sqrt{}6 /10 s

therefore, v=s/t => 2.45 m/s

Where did i go wrong? The given answer is 2 m/s and i don't believe that its an approximation.

 

[HallsofIvy]

I don't really see what you are doing. You start off by assuming that u, the initial vertical speed, is 0, which is true, and caluculate the time it will take to go down 0.3 meters. Finally, you calculate the average speed over that time. That was not what was asked. You are asked for the initial horizontal speed, ux, required so that the ball hits the lowest step. That is, you must find u such that the ball misses the second step. When the vertical drop is 0.2 meters, the horizontal motion must be at least 0.4 m. You have two equation: (1/2)at^2= 0.2, ux t= 0.4. Solve for ux.

 

[Saitama]

You did the last step wrong. You can't perform v=s/t because acceleration is there in the situation. But that's not for initial velocity asked in the question. Follow HallsofIvy advise.

 

[AlchemistK]

Ahhh yes, i get it now, thank you.