A ball is thrown in the air so that $t$ seconds after it is thrown, its height $h$ metre above its starting point is given by the polynomial $h=25 t-5 t^{2}$. Observe the graph of the polynomial and answer the following questions: (i) Write zeroes of the given polynomial. 1 (ii) Find the maximum height achieved by ball. 1 (iii)(a) After throwing upward, how much time did the ball take to reach to the height of $30 \mathrm{~m} ? 2$
Explanation
This question asks us to find the time it takes for the ball to reach a height of 30 m. We can use the given polynomial to find the time: 25t - 5t^2 = 30. Rearranging this equation, we get 5t^2 - 25t + 30 = 0. Solving this quadratic equation, we get two possible values of t: t = 2.5 s and t = 3.5 s.
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