Question

Peter is a painter, and he wonders if he would have time to catch a paint bucket dropped from his ladder before it hits the ground. He drops a bucket from the top of his 9-foot ladder. The height, h, of the bucket can be represented by the equation, h= -16t^2 + 9, where the height is measured in feet from the ground, and the time since the bucket was dropped, t, is measured in seconds. After how many seconds does the bucket hit the ground? Do you think he could catch the bucket before it hits the ground.

Answer 1

When the bucket hits the ground, h = 0.  Therefore, set h= -16t^2 + 9 = 0 and solve the resulting equation for t:
                             9
16t^2 = 9;  t^2 = ----- ;  taking the positive square root of both sides, t = 3/8 sec
                            16

Think the painter could or could not catch the bucket in 3/8 sec or less?