PART A
The given equation is

In order to find the maximum height, we write the function in the vertex form.
We factor -16 out of the first two terms to get,

We add and subtract

to get,

We again factor -16 out of the first two terms to get,

This implies that,

The quadratic trinomial above is a perfect square.

This finally simplifies to,

The vertex of this function is

The y-value of the vertex is the maximum value.
Therefore the maximum value is,

PART B
When the ball hits the ground,

This implies that,

We add -29 to both sides to get,

This implies that,




or

Since time cannot be negative, we discard the negative value and pick,