Q)  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 – 16t2. Based on the above, answer the following questions:
(i) Find zeroes of polynomial p(t) = 20t – 16t².
(ii) Which of the following types of graph represents p(t)? (iii) (a) What would be the value of h at t = ? Interpret the result.

Or

(iii) (b) How much distance has the dolphin covered before hitting the water level again?

Ans:

(i) Zeroes of the polynomial:

Given polynomial equation is p(t): 20t – 16t2 = 0

or -16 t2  + 20 t = 0

Let the roots of the polynomial be α and β.

We know that sum of roots (α + β) =  α + β = = Next, we know that the product of the roots (α x β) = α . β =  α = 0, β = (ii) Graph of p(t):

We just calculated that roots of the equation and hence, values of t = 0, It clearly means the value of the polynomial should be zero at these values of t.

If we note the 4 graphs, Option B is not zero at t = . Therefore, B is not the option.

Next, let’s check the values of t between 0 and or 1.25

Let’s put t = 0.5 in the polynomial, we get:

p(0.5) = 20 (0.5) – 16 (0.5) = 10 – 4 = 6

If we note the 4 graphs, only option A shows positive value at t = 0.5 whereas option C and D are showing negative values. Therefore, A is the correct option whereas C and D are incorrect.

(iii) (a) Value at t = :

Value of p(t) at t = :   20 – 16 = 30 – 36 = – 6

Interpretation: It means that at t = , the dolphin is 6m below water level.

(iii)(b): Distance travelled by dolphin before hitting water level again:

The Dolphin hits the water level in seconds.

Given that the speed of the dolphin = 20 cm per second

It means, in one second, distance covered = 20 cm in seconds, distance covered will be

= x 20

= 25 cm

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