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In a pool at an aquarium, a dolphin jumps out of the water travelling at $20$ cm per second. Its height above water level after $t$ seconds is given by $h = 20t - 16t^2$.
Based on the above, answer the following questions :
(i) Find zeroes of polynomial $p(t) = 20t - 16t^2$.
(ii) Which of the following types of graph represents $p(t)$?
(iii) (a) What would be the value of $h$ at $t = \frac{3}{2}$ ? Interpret the result.
OR
(iii) (b) How much distance has the dolphin covered before hitting the water level again?
Based on the above, answer the following questions :
(i) Find zeroes of polynomial $p(t) = 20t - 16t^2$.
(ii) Which of the following types of graph represents $p(t)$?
(iii) (a) What would be the value of $h$ at $t = \frac{3}{2}$ ? Interpret the result.
OR
(iii) (b) How much distance has the dolphin covered before hitting the water level again?
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(i) $-16t^2 + 20t = 0 \Rightarrow 4t(-4t + 5) = 0$
$t = 0, t = \frac{5}{4}$
(ii) (a)
(iii)(a) At $t = \frac{3}{2}$, $h = -16 \times \frac{9}{4} + 20 \times \frac{3}{2} = -36 + 30 = -6$
It means after $\frac{3}{2}$ seconds, dolphin has reached $6$ cm below water level.
OR
(iii)(b) Speed of dolphin $= 20$ cm per second.
In one second, distance covered $= 20$ cm
In $\frac{5}{4}$ seconds, distance covered $= 20 \times \frac{5}{4} = 25$ cm
$t = 0, t = \frac{5}{4}$
(ii) (a)
(iii)(a) At $t = \frac{3}{2}$, $h = -16 \times \frac{9}{4} + 20 \times \frac{3}{2} = -36 + 30 = -6$
It means after $\frac{3}{2}$ seconds, dolphin has reached $6$ cm below water level.
OR
(iii)(b) Speed of dolphin $= 20$ cm per second.
In one second, distance covered $= 20$ cm
In $\frac{5}{4}$ seconds, distance covered $= 20 \times \frac{5}{4} = 25$ cm