Confused with question

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)=-16t^2 +48t +160 models the h, and the rock above the ocean as function of time t. Find

a. The zeroes of this function that tells 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

h()= 0 , h()= and h()=160ft , h(1.5)=

Answer 1

a) the rock hits the ocean when the height of the rock is 0

0=-16t^2+48t+160

16t^2-48t-160=0

t^2-3t-10=0

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

t-5=0

t=5 seconds

b) 160=-16t^2+48t+160

subtract 160 from both sides

0=-16t^2+48t

16t^2-48t=0

t^2-3t=0

t(t-3)=0

t=0, right before she throws the rock because she is 160 feet above the ocean, and....

t-3=0

t=3 seconds after she throws the rock (the rock will go up and then start to come down and after 3 seconds the rock will be 160 feet above the ocean)

c) h(1.5)=-16(1.5)^2+48(1.5)+160

h(1.5)=-16(2.25)+72+160

h(1.5)=-36+72+160

h(1.5)=196 feet above the ocean after 1.5 seconds