CBSE Class 10 Maths (Standard) 2023 · Paper 30/5/1 · Question 38

Polynomials 4 marks Hard

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 = 20 t - 16 t^{2}

. Based on the above, answer the following questions :

Option (a) candidate graph.

Option (b) candidate graph.

Option (c) candidate graph.

Option (d) candidate graph.

(i)Find zeroes of polynomial $p (t) = 20 t - 16 t^{2}$ .[1]
(ii)Which of the following types of graph represents $p (t)$ ?[1]
(iii) (a)What would be the value of $h$ at $t = \frac{3}{2}$ ? Interpret the result.[2]
(iii) (b)How much distance has the dolphin covered before hitting the water level again ?[2]

Answer

(i)

t = 0, \frac{5}{4}

; (ii) Downward parabola (option a); (iii)(a)

h = - 6

(6 cm below water); (iii)(b)

12.5

cm vertical path

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