When a slice of buttered toast is accidentally pushed over the edge of a counter, it rotates as it falls. If the distance to the floor is 76 cm and for rotation less than 1 rev, what are the (a) smallest and (b) largest angular speeds that cause the toast to hit and then topple to be butter-side down?

Explanation

To solve the problem of the buttered toast falling off the counter and determining the smallest and largest angular speeds that cause it to hit and then topple butter-side down, we will follow these steps:

### Step 1: Calculate the time of fall
We know the height \( h = 0.76 \, \text{m} \) and the acceleration due to gravity \( g = 10 \, \text{m/s}^2 \). The time \( t \) it takes to fall can be calculated using the formula:
\[ t = \sqrt{\frac{2h}{g}} \]
Substituting the values:
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