Answer to Question #140671 in Calculus for stuti patel

Question

the height of an object falling from a cliff is given by h(t)= 520 - 30t -16t^2. the time measurement is correct to within 0.25 seconds. estimate the propagated error in computing the height of the object at time t=3 sec.

Answer 1

h(t) = 520-30t-16t² equalization of height

h(3)= 520-30*3-16*9 = 286 with accurate timing

if 0,25 exactness at times

then time will belong to the interval

t = 3 ± 0.25

t_min =3-0.25

t_max=3+0.25

then a height will be scope

h(3-0.25) = 520-30*2.75-16*2.75² = 316.5 max

h(3+0.25) = 520-30*3.25-16*3.25² = 253.5 min

mean value

h₀ = ( h_min+h_max)/2 = 285

exactness is equal to the half of interval

$\Delta$ = ( h_max- h_min+)/2 = 31.5

then get

h = h₀ ± $\Delta$ = 285 ± 31.5