Question

A diver is standing on a platform 24ft. Above the pool. He jumps from the platform with an initial upward velocity of 8ft/s. Use the formula h(t)=-16^2+vt+s, where h is his height above the water, t is the time, v is his starting upward velocity, and s is his starting height. How long will it take for him to hit the water?

Answer 1

Answer: The answers is 1.5 second

Answer 2

He will take 1.5 seconds to hit the water

Explanation:

* The formula h(t) = -16t² + vt + s

- h is the his height above the water

- v is his initial up-word velocity

- s is his starting height

- t is the time

* When he hits the water h(t) = 0

- because h is his height above the water

∴ -16t² + vt + s = 0

∵ v = 8 ft/s

∵ s = 24 ft

∴ -16t² + 8t + 24 = 0 ⇒ × (-1)

∴ 16t² - 8t - 24 = 0 ⇒ ÷ 8

∴ 2t² - t - 3 = 0 ⇒ by using factorization

∴ (2t - 3)(t + 1) = 0

∴ 2t - 3 = 0 ⇒ 2t = 3 ⇒ t = 3/2 = 1.5 sec

∴ t + 1 = 0 ⇒ t = -1 ⇒ rejected the time is positive value

* He will take 1.5 seconds to hit the water