+448 The height, in metres, of a toy rocket launched at an initial upward velocity of 30 m/s, from a
height of 1 m, is approximately given by
h=-4.9t^2+30t+1
where t is measured in seconds.
a) Determine the difference quotient for this
function and use it to determine the AROC of
the rocket from t = 4 s to t = 6 s.
b) Determine the IROC of the rocket at t = 5 seconds.
+129852 a) We don't need the difference quotient for this one
Average rate of change = h(6) -h(4)
__________
6 - 4
h(6) = -4.9(6)^2 + 30(6) + 1 = 4.6
h(4) = -4.9(4)^2 + 30 (4) + 1 = 42.6
So
Avg rate of change = [ 4.6 - 42.6] -38
___________ = _______ = -19ft / s
6 - 4 2
b) Difference Quotient
f ( t + h) - f(t)
____________
h
f ( t + h) = -4.9 ( t + h)^2 + 30 (t + h) + 1 = -4.9t^2 - 9.8th - 4.9h^2 + 30 t + 30 h + 1
f ( t) = -4.9t^2 + 30t + 1
So
[ -4.9t^2 - 9.8 th - 4.9h^2 + 30t + 30 h +1 ] - [ -4.9t^2 + 30t + 1 ]
______________________________________________________ =
h
-9.8 th + 30h
___________ =
h
h ( -9.8t + 30)
____________ = -9.8t + 30
h
Instantaneous rate of change at 5 sec = -9.8(5) + 30 = -19 ft/s
