Standing on the roof of a (42.0+a) m tall building, you throw a ball straight up with an initial speed of (14.5+b) m/s. if the ball misses the building on the way down, how long will it take from you threw the ball until it lands on the ground below? give your answer in seconds and round the answer to three significant figures.

First, we must find the vertical distance traveled upwards by the ball due to the throw. For this, we will use the formula:

2as = v² - u²

Because the final velocity v is 0 in such cases

s = -u²/2a; because both u and a are downwards, the negative sign cancels

s = 14.5² / 2*9.81
s = 10.72 meters

Next, to find the time taken to reach the ground, we need the height above the ground. This is:
45 + 10.72 = 55.72 m

We will use the formula 
s = ut + 0.5at²

to find the time taken with the initial velocity u = 0.

55.72 = 0.5 * 9.81 * t²

t = 3.37 seconds

If football was tossed in air without gravity or friction the ball would go into space