Question

Consider the shuttle carrying the astronauts is dropped from 100ft. The position 𝑠 of the shuttle is given by the following function as a function of time: 𝑠(𝑡) = −16𝑡 2 + 100

Consider the interval [0, c] where 0 is the time when the shuttle drops, and c is the time when the shuttle hits the surface of the Earth. Find the height or position of the shuttle when time is: 0, 0.5, 1, 1.5, 2, and 2.5 seconds. What is the domain of this function? Also, sketch the graph of the position s. 

Answer 1

$$s(t)=-16t^2+100$$

$$s(0)=-16(0)^2+100=100 (ft)$$

$$s(0.5)=-16(0.5)^2+100=96 (ft)$$

$$s(1)=-16(1)^2+100=84 (ft)$$

$$s(1.5)=-16(1.5)^2+100=64 (ft)$$

$$s(2)=-16(2)^2+100=36 (ft)$$

$$s(2.5)=-16(2.5)^2+100=0 (ft)$$

$Domain:[0,2.5]$