Cherrybunchviz
Answered

Careena likes throwing rocks at the ocean. When she throws the rocks upward from 160 ft above the ocean, h(t)= -16t²+48t+160 models the height, h, of the rock above the ocean as a function of time, t, in seconds. How long will it take the rock to reach the ocean (h=0)?​

Sagot :

MindOverMatterviz

Answer:

Hey!

196 ft. above the ocean at 1.5 sec.

Step-by-step explanation:

Solution :

Given = [tex]h(t) = - {16t}^{2} + 48t + 160[/tex]

  • Zeroes equate h(t) to zero that is [tex] - {16t}^{2} + 48t + 160 = 0[/tex] (divide by -16)

  • [tex] {t}^{2} - 3t - 10 = 0[/tex] (Factorized function of) [tex] - {16t}^{2} + 48t + 160 = 0[/tex].

  • (t - 5) (t + 2) = 0
  • t = 5 , -2

However t > 0 ⇒ t = 5 is when the rock hits the ocean.

  • Substitute t ⇒ 1.5 into h(t)

Then...

  • h(1.5) ⇒ [tex] - 16{(1.5)}^{2} + 4.8(1.5) + 160[/tex]
  • ⇒ -36 + 72 + 160 ⇒ 196

The rock is 196 ft. above the ocean on 1.5 sec.

Therefore 196 ft. above the ocean at 1.5 sec.

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