A ball bearing is projected upwards from the ground with a velocity of 15 ms^-1. Calculate the time taken by the ball to return to the ground.

Sure, let's solve this step by step.

1. First, we need to understand that the ball bearing is projected upwards and then it returns back to the ground. This is a case of motion under gravity.

2. In such cases, the initial velocity (u) is 15 m/s (upwards), the final velocity (v) is 0 m/s (at the highest point), and the acceleration (a) is -9.8 m/s² (downwards, due to gravity).

3. We can use the first equation of motion to find the time taken to reach the highest point: v = u + at. Rearranging for t gives us t = (v - u) / a.

4. Substituting the known values, we get t = (0 - 15) / -9.8 ≈ 1.53 seconds. This is the time taken to reach the highest point.

5. However, the ball takes the same amount of time to come back down. So, the total time taken by the ball to return to the ground is 2 * 1.53 = 3.06 seconds.

So, the ball bearing takes approximately 3.06 seconds to return to the ground.