A cement block accidentally falls from rest from the ledge of a 51.6 -m-high building. When the block is 15.7 m above the ground, a man, 1.90 m tall, looks up and notices that the block is directly above him. How much time, at most, does the man have to get out of the way?

Question

A cement block accidentally falls from rest from the ledge of a 51.6 -m-high building. When the block is 15.7 m above the ground, a man, 1.90 m tall, looks up and notices that the block is directly above him. How much time, at most, does the man have to get out of the way?

Answer 1

h(t) = 51.6 - 4.9t^2

we want the time between when
h(t) = 15.7 and
h(t) = 1.90

So, just solve for t in

51.6-4.9t^2 = 15.7
51.6-4.9t^2 = 1.90

and subtract to find how long it will take to crush the man's skull.