How Fast Was the Baseball Rolling Before It Fell?

[yankee]

An autographed baseball rolls off a 1.2m high desk & strikes the floor 0.37m away from the desk. The acceleration of gravity is 9.81m/s^2. How fast was it rolling on the desk before it fell off?

 

[kreil]

Analyze the problem vertically using the equation

d=v_it+\frac{1}{2}at^2

since vi is zero, solving for time yields:

d=\frac{1}{2}at^2 \implies t=\sqrt{\frac{2d}{a}}

Now, use this time to analyze the problem horizontally. It moved a total distance d in time t, so use the equation

v_i=\frac{d}{t}

and this will yield the balls initial horizontal velocity.