An object is thrown upward. Its height is a function of time, h(t) as shown in the table below.

Question

An object is thrown upward. Its height is a function of time,h(t)as shown in the table below.

h (ft)	0	19	36	51	64	75	84	91	96	99	100
t (s)	0.00	0.25	0.50	0.75	1.00	1.25	1.50	1.75	2.00	2.25	2.50

Graph the function on the domain 0 ≤ t ≤ 2.5

seconds. After your graph is complete answer the following questions:

1. As time passes, is the height increasing or decreasing?
2. As time passes, is the the object speeding up or slowing down?
3. At which time is the height greater: t = 1 second or t = 2 seconds?
4. At which time is the velocity greater: t = 1 second or t = 2 seconds?

  

Answer 1

plot the points on a graph, t on the horizontal or x axis, h on the vertical or y axis. connect them with a smooth curve. It should be a parabolic shape, upward opening, but only the left half of a parabola. t= 2.5 (2.5, 100) is the maximum point or vertex of the parabola.

as time passes, the height increases, but its speed slows down from t=0 to t= 2.5

the height is greater at 2 seconds than at 1 second 96 ft >64 ft

but velocity is greater at t=1 than t=2

velocity at t= 1 is 48 ft/sec

velocity at t =2 is 16 ft/sec

velocity at t = 2.5 is 0 ft/sec

equation for the height is h(t) = -16t^2 + 80t

equation for velocity = the derivative or h(t) =

h'(t) = -32t + 80