6. A ball is hit into the air. Its height, $h$, in metres after $t$ seconds can be modeled by $h=-5 t^{2}+40 t+1$ a) What is the maximum height of the ball? [2] b) How long does the ball take to reach this height? [2] c) What is the initial height of the ball? [1]

Step 1 ：\(-5t^2+40t+1=-5(t^2-8t)+1\)

Step 2 ：\(-5(t^2-8t)+1=-5(t^2-8t+16-16)+1\)

Step 3 ：\(-5(t^2-8t+16-16)+1=-5([t-4]^2-16)+1\)

Step 4 ：\(-5(t-4)^2+81\)

Step 5 ：\boxed{81}

Step 6 ：\(t=4\)

Step 7 ：\(h(0)=-5(0)^2+40(0)+1\)

Step 8 ：\boxed{1}