Question

Case Study -1

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 that h(t) = -16t² + 8t + k.

At what time will she touch the water in the pool?

विकल्प

• 30 seconds

• 2 seconds

• 1.5 seconds

• 0.5 seconds

Answer 1

2 seconds

Explanation:-

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 = 2 seconds