Arock is thrown vertically upward from ground level at time t = 0. at t = 1.6 s it passes the top of a tall tower, and 1.0 s later it reaches its maximum height. what is the height of the tower?

The rock has height at time according to

where is the velocity with which it was thrown, and g = 9.8 m/s^2 is the acceleration due to gravity.

Complete the square to get

which indicates a maximum height of occurs when . We're told this time is 2.6 s after the rock is thrown:

So when t = 1.6 s, the rock reaches the tower's height of