If a rock falls freely (without air-resistance) to the ground from a height of 20-feet on Earth, the height 𝐻 (in feet) after 𝑡 seconds, is given by the function 𝑯(𝒕)= 𝟐𝟎−𝟏𝟔𝒕𝟐.

Question

a) Solve H(t) < 4

 

b) In your own words, what does your answer to part (a) represent in relation to the problem?

Answer 1

H(t) = 20-16t^2 < 4

-16t^2 < -16

t^2 > 1

t > 1 or t<-1, ignore the -1

It means you have to wait over 1 second to have the height be less than 4 feet

Less than 1 second and the rock is over 4 feet high

the rock goes from 20 feet high to 4 feet high in one second

It travels 16 feet in one second