Aball is projected upward at time t = 0.00 s from a point on a roof 70 m above the ground. the ball rises, then falls and strikes the ground. the initial velocity of the ball is 82 m/s if air resistance is negligible. the time when the ball strikes the ground is closest to

17.68 s

Explanation:

This problem is a good example of Vertical motion, where the main equation for this situation is:  

(1)  

Where:  

is the height of the ball when it hits the ground  

is the initial height of the ball

is the initial velocity of the ball  

is the time when the ball strikes the ground

is the acceleration due to gravity  

Having this clear, let's find from (1):  

(2)  

Rewritting (2):

(3)  

This is a quadratic equation (also called equation of the second degree) of the form , which can be solved with the following formula:

 (4)

Where:

Substituting the known values:

 (5)

Solving (5) we find the positive result is: