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.

Step 1: Understand the problem The ball bearing is projected upwards and we need to find the time it takes to return to the ground. This is a problem of motion under gravity.

Step 2: Identify the knowns The initial velocity (u) of the ball is given as 15 m/s. The acceleration due to gravity (g) is -9.8 m/s² (negative because it acts downwards). The final position of the ball is the ground, so the final displacement (s) is 0.

Step 3: Identify the unknown The time (t) it takes for the ball to return to the ground is what we need to find.

Step 4: Choose the appropriate equation of motion We can use the second equation of motion, which is s = ut + 0.5gt².

Step 5: Substitute the known values into the equation 0 = (15 m/s * t) + 0.5 * (-9.8 m/s²) * t²

Step 6: Solve the equation for t This is a quadratic equation in the form of 0 = at² + bt + c. We can solve it using the quadratic formula t = [-b ± sqrt(b² - 4ac)] / 2a.

In this case, a = -4.9 m/s², b = 15 m/s, and c = 0. So, t = [-15 ± sqrt((15)² - 4*(-4.9)0)] / 2(-4.9).

Solving this gives two solutions, t = 3.06 s and t = 0 s. The time cannot be 0 because that would be the moment the ball was projected. So, the time it takes for the ball to return to the ground is 3.06 seconds.