What is the time and speed of a rolling ball from tabletop to floor?

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SUMMARY

The discussion focuses on calculating the time a small ball is in the air after rolling off a tabletop 1.22 m high and landing 1.58 m away horizontally. To determine the time of flight, participants emphasize using the vertical motion equation, specifically y(t) = y0 + v_y*t + (1/2)*a*t^2, where the initial vertical velocity is zero and acceleration is due to gravity. Once the time is established, the horizontal speed can be calculated using the formula for constant velocity, where speed equals distance divided by time.

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Homework Statement


A small ball rolls horizontally off the edge of a tabletop that is 1.22 m high. It strikes the floor at a point 1.58 m horizontally away from the edge of the table. (a) How long is the ball in the air? (b) What is its speed at the instant it leaves the table?



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The Attempt at a Solution


So far all I've been able to calculate is the distance from the tabletop to the position on the floor that it landed. = 1.99m. Is there some equation with a trig function in it to get the time the ball is in the air?
 
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You have to split the motion into x and y components. The x motion is constant velocity and the y motion is uniformly accelerated downward. Stuff like y(t)=y0+v_y*t+(1/2)*a*t^2. Surely you know of stuff like that. No trig functions in this one.
 
For (a) all you need to know is how long the ball was in the air. Consider the ball along the y direction only. What is the inital velocity, displacement and acceleration? Stick thoose values into an equation of motion to find the value of time.

For (b) once you know the time the ball is in the air the rest should be easy. This time consider the ball only along the x axis. What would it's velocity have to be if it were to travel 1.58m in the time you calculated for (a).
 
Thanks, I do appreciate it.
 

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