Question

Genevieve is going to throw a rock from the top of a trail overlooking the ocean. When she throws the rock upward from 160 feet above the ocean, the function h(t)=−16 t 2 +48t+160 models the height, h , of the rock above the ocean as a function of time, t . Find a. the zeros of this function that tell us when the rock will hit the ocean. b. when the rock will be 160 feet above the ocean. c. the height of the rock at t=1.5 seconds.

Answer 1

I don't know

if you know please tell me also

Answer 2

(a) t = 5 seconds

(b) t = 0 seconds and t = 3 seconds

(c) h(1.5) = 196 feet.

Step-by-step explanation:

The function h(t) = − 16t² + 48t + 160 ........... (1)  gives the height, h , as a function of time, t where h(t) is in feet and t is in seconds.

a) The zeros of the function are given by

0 = − 16t² + 48t + 160

⇒ 16t² - 48t - 160 = 0

⇒ t² - 3t - 10 = 0

⇒ (t - 5)(t + 2) = 0

⇒ t = 5 seconds.

Since, t ≠ negative.

b) 160 = − 16t² + 48t + 160

⇒ - 16t² + 48t = 0

⇒ t = 0 and t = 3

So, at t = 0 seconds and at t= 3 seconds, the rock will be at height 160 feet.

c) Putting t = 1.5 seconds we get, h(1.5) = - 16 (1.5)²  + 48 × 1.5 + 160 = 196 feet. (Answer)