At time t = 0, a rotating bicylce wheel is thrown horizontally from a rooftop with a speed of 49 m/s. By the time its vertical speed is also 49 m/s, it has completed 40 revolutions. What has been its average angular speed to that point in the fall?

Explanation

To solve the problem, we need to find the average angular speed of the bicycle wheel after it has completed 40 revolutions while falling from a rooftop. Let's break down the solution step by step:

### Step 1: Understand the Problem
The bicycle wheel is thrown horizontally with an initial horizontal speed of 49 m/s. As it falls, it also gains vertical speed due to gravity. By the time its vertical speed reaches 49 m/s, it has completed 40 revolutions.

### Step 2: Determine the Time of Fall
We can use the equation of motion for vertical motion under gravity to find the time taken to reach a vertical speed of 49 m/s. The equation is:

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