if a stone is dropped from a heightof 400 ft then its height

if a stone is dropped from a heightof 400 ft, then its height (in feet) above the ground is given by the function

h(t)= -16t^2 + 400 where t is time (in seconds). To get an idea how fast the stone is traveling when it hits the ground, find the average rate of change of the height on each of the time intervals [0,5],[1,5],[4.99,5], and [4.999,5]

the average rate of change of the height on the interval [0,5] is ? ft/sec

Solution

h(t)= -16t^2 + 400

average rate of change of the height on the interval [0,5]=[h(5)-h(0)]/(5-0)

average rate of change of the height on the interval [0,5]=[( -16*5^2 + 400)-(-16*0^2 + 400)]/(5-0)

average rate of change of the height on the interval [0,5]=-80ft/s

average rate of change of the height on the interval [1,5]=[h(5)-h(1)]/(5-1)

average rate of change of the height on the interval [1,5]=[( -16*5^2 + 400)-(-16*1^2 + 400)]/(5-1)

average rate of change of the height on the interval [1,5]=-96ft/s

average rate of change of the height on the interval [4.99,5]=[h(5)-h(4.99)]/(5-4.99)

average rate of change of the height on the interval [4.99,5]=[( -16*5^2 + 400)-(-16*4.99^2 + 400)]/(5-4.99)

average rate of change of the height on the interval [4.99,5]=-159.84ft/s

average rate of change of the height on the interval [4.999,5]=[h(5)-h(4.999)]/(5-4.999)

average rate of change of the height on the interval [4.999,5]=[( -16*5^2 + 400)-(-16*4.999^2 + 400)]/(5-4.999)

average rate of change of the height on the interval [4.999,5]=-159.984ft/s