Question

11. A diver jumps from a platform. The situation is best modeled by

h=-9t² + 15t+7, where h is the height of the diver above water in meters and t is the time in
seconds. How long will it take for the diver to hit the water? Round to the nearest hundredth

Answer 1

2.05 secs

Explanation:

we will use quadratic formula to work out the time t.

t = ((-b ± √(b² - 4ac)) ÷ 2a)

where a is the value of the first coefficient, b is value of the second and c is value of the constant.

h = -9t² + 15t + 7

we need water level, so h = 0.

-9t² + 15t + 7 = 0

a = -9, b = 15, c = 7.

t = ((-b ± √(b² - 4ac)) ÷ 2a)

= ((-(15) ± √((15)² - 4(-9)(7))) ÷ 2(-9))

= ((-15 ± √(225 - -252)) ÷ -18)

= ((-15 ± √(225 + 252)) ÷ -18)

= ((-15 ± √(477)) ÷ -18)

= -0.380 or 2.05

t is time, so it has to be positive.

t = 2.05 seconds to nearest one hundredth