At what time will she touch the water in the pool? (a) 30 seconds (b) 2 seconds (c) 1.5 seconds (d) 0.5 seconds
Answers
SOLUTION
GIVEN
- Annie was standing on a diving board 48 feet above the water level
- She took a dive into the pool . Her height in feet in water level at any time t sec is given by the polynomial
h(t) = - 16t² + 8t + k
TO DETERMINE
- The value of k.
- The time will she touch the water in the pool
EVALUATION
Here the given polynomial is
h(t) = - 16t² + 8t + k
ANSWER TO QUESTION : 1
By the given condition h(0) = 48
Again h(0) = - 16 × 0² + 8 × 0 + k
⇒ 48 = k
⇒ k = 48
Hence the required value of k = 48
ANSWER TO QUESTION : 2
We have to find the value of t where h(t) = 0
Now the given polynomial is
h(t) = - 16t² + 8t + 48
Now h(t) = 0
⇒- 16t² + 8t + 48 = 0
⇒ 2t² - t - 6 = 0
⇒ 2t² - 4t + 3t - 6 = 0
⇒ ( t - 2 ) ( 2t + 3 ) = 0
t - 2 = 0 gives t = 2
2t + 3 = 0 gives t = - 3/2
Since time can not be negative
So t = 2
Hence the required time = 2 seconds
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Answer:
GIVEN
Annie was standing on a diving board 48 feet above the water level
She took a dive into the pool . Her height in feet in water level at any time t sec is given by the polynomial
h(t) = - 16t² + 8t + k
TO DETERMINE
The value of k.
The time will she touch the water in the pool
EVALUATION
Here the given polynomial is
h(t) = - 16t² + 8t + k
ANSWER TO QUESTION : 1
By the given condition h(0) = 48
Again h(0) = - 16 × 0² + 8 × 0 + k
⇒ 48 = k
⇒ k = 48
Hence the required value of k = 48
ANSWER TO QUESTION : 2
We have to find the value of t where h(t) = 0
Now the given polynomial is
h(t) = - 16t² + 8t + 48
Now h(t) = 0
⇒- 16t² + 8t + 48 = 0
⇒ 2t² - t - 6 = 0
⇒ 2t² - 4t + 3t - 6 = 0
⇒ ( t - 2 ) ( 2t + 3 ) = 0
t - 2 = 0 gives t = 2
2t + 3 = 0 gives t = - 3/2
Since time can not be negative
So t = 2
Hence the required time = 2 seconds