Q:

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)=−16t2+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.

Accepted Solution

A:
Answer:see explanationStep-by-step explanation:Givenh(t) = - 16t² + 48t + 160(a)To find the zeros equate h(t) to zero, that is- 16t² + 48t + 160 = 0 ( divide through by - 16 )t² - 3t - 10 = 0 ← in standard form(t - 5)(t + 2) = 0 ← in factored formEquate each factor to zero and solve for tt - 5 = 0 ⇒ t = 5t + 2 = 0 ⇒ t = - 2However t > 0 ⇒ t = 5 is when the rock hits the ocean(b)Equate h(t) to 160- 16t² + 48t + 160 = 160 ( subtract 160 from both sides )- 16t² + 48t = 0 ( divide through by - 16 )t² - 3t = 0 ← factor out t from each termt(t - 3) = 0t = 0 ← time when rock was thrown from the top of the trailt - 3 = 0 ⇒ t = 3 The rock is 160 ft above the ocean at 0 seconds and 3 seconds(c)Substitute t = 1.5 into h(t)h(1.5) = - 16(1.5)² + 48(1.5) + 160 = - 36 + 72 + 160 = 196The rock is 196 ft above the ocean at 1.5 seconds