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The figure given alongside shows the path of a diver, when she takes a jump from the diving board. Clearly it is a parabola.Annie was standing on a diving board, 48 feet above the water level. She took a dive into the pool. Her height (in feet) above the water level at any time‘t’ in seconds is given by the polynomial h(t) such thath(t) = -16t2 + 8t + k.1. What is the value of k?(a) 0(b) - 48(c) 48(d) 48/-162. At what time will she touch the water in the pool?(a) 30 seconds(b) 2 seconds(c) 1.5 seconds(d) 0.5 seconds3. Rita’s height (in feet) above the water level is given by another polynomial p(t) with zeroes -1 and 2. Then p(t) is given by-(a) t2 + t - 2.(b) t2 + 2t - 1(c) 24t2 - 24t + 48.(d) -24t2 + 24t + 48.4. A polynomial q(t) with sum of zeroes as 1 and the product as -6 is modelling Anu’s height in feet above the water at any time t( in seconds). Then q(t) is given by(a) t2 + t + 6(b) t2 + t -6(c) -8t2 + 8t + 48(d) 8t2 - 8t + 485. The zeroes of the polynomial r(t) = -12t2 + (k-3)t +48 are negative of each other. Then k is(a) 3(b) 0(c) -1.5(d) -3 |
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Answer» 1. Correct answer is: (c) 48 Initially, at t=0, Annie’s height is 48ft So, at t =0, h should be equal to 48 h(0) = -16(0)2 + 8(0) + k = 48 So k = 48 2. Correct answer is: (b) 2 seconds When Annie touches the pool, her height =0 feet i.e. -16t2 + 8t + 48 =0 above water level 2t2 - t -6 =0 2t2 - 4t +3t -6 =0 2t(t-2) +3(t-2) =0 (2t +3) (t-2) =0 i.e. t= 2 or t= -3/2 Since time cannot be negative , so t= 2seconds 3. Correct answer is: (d) -24t2 + 24t + 48. t= -1 & t=2 are the two zeroes of the polynomial p(t) Then p(t)=k (t- -1)(t-2) = k(t +1)(t-2) When t = 0 (initially) h1 = 48ft p(0)=k(02- 0 -2)= 48 i.e. -2k = 48 So the polynomial is -24(t2- t -2) = -24t2 + 24t + 48. 4. Correct answer is: (c) -8t2 + 8t + 48 A polynomial q(t) with sum of zeroes as 1 and the product as -6 is given by q(t) = k(t2 - (sum of zeroes)t + product of zeroes) = k(t2 -1t + -6) ………..(1) When t=0 (initially) q(0)= 48ft q(0)=k(02- 1(0) -6)= 48 i.e. -6k = 48 or k= -8 Putting k = -8 in equation (1), reqd. polynomial is -8(t2 -1t + -6) = -8t2 + 8t + 48 5. Correct answer is: (a) 3 When the zeroes are negative of each other, sum of the zeroes = 0 So, -b/a = 0 \(-\cfrac{(k-3)}{-12}=0\) \(+\cfrac{(k-3)}{12}=0\) k-3 = 0, i.e. k = 3. |
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