Let's solve this step by step using completing the square.

Given equation:

$h = 32t - 16t^2 + 4$ We need to find $t$ when $h = 20$: $20 = 32t - 16t^2 + 4$ Rearrange: $-16t^2 + 32t + 4 - 20 = 0$ $-16t^2 + 32t - 16 = 0$ Divide by $-16$ to simplify: $t^2 - 2t + 1 = 0$

Completing the square:

$(t - 1)^2 = 0$ Solving for $t$: $t - 1 = 0 \Rightarrow t = 1$

Thus, the ball reaches 20 ft at $t = 1$ second.

Would you like a more detailed breakdown or an alternative solution?

Related Questions:

1. How do you complete the square for any quadratic equation?
2. What is the vertex form of the given quadratic equation?
3. Can the ball reach 20 ft at any other time besides $t = 1$?
4. What is the maximum height reached by the ball?
5. How do you find the time at which the ball reaches its maximum height?

Tip:

When solving quadratics by completing the square, always factor out the coefficient of $t^2$ before completing the square!