2026 ZHSS P2 Q10

A student stands on the roof of a building and throws a ball upward. The height of the ball above the ground, \(h\) metres, at time \(t\) seconds after it is thrown, is modelled by \(h=15-5t^2+10t\).

1. Express \(h\) in the form \(h=a(t-b)^2+c\), where \(a\), \(b\) and \(c\) are constants.[3]
2. Hence, find the maximum height reached by the ball and the time at which this occurs.[2]
3. A bird is perched at a height of \((k+10)\) metres above the ground. The ball hits the bird at \(t=1+\dfrac k5\) seconds. Find the value of \(k\).[4]