Applications of the Initial Value Problem y' = f(:r, y); y(c) = d 14514012010080
y(x)
6040200(^0 2 4) x 6 8
Figure 3.13 Numerical Approximation to the IVP:
y' = 32 - .25y; y(O) = 20
EXERCISES 3 .5
10
l. Write the equation for the velocity of a falling body, if the air resist-
ance is proportional to the squ are of the velocity. Numerically compute
and graph the velocity on the interval [O, 10], if g = 32 ft/sec^2 , if the
constant of proportionality is c = .25, and if the initial velocity is v(O) =
20 ft/sec. Estimate the terminal velocity in this case.- Write the differential equation for the velocity of a falling body, if t he
air resistance is proportional to vl.^6. Numerically compute and graph
the velo city on the interval [O, 10], if g = 32 ft/sec^2 , if the constant of
proportionality is c = .25, and if the initial velocity is v(O) = 20 ft/sec.
Estimate the terminal velocity.- Write the differential equation for the velocity of a falling body, if the
air resistance is proportional to -JV. Compute and graph the velocity on
the interval [O, 10], if g = 32 ft/sec^2 , if the constant of proportionality is
c = .25, and if the initial velocity is v(O) = 20 ft/sec. Is there a terminal
velocity? If so, estimate its value. - A parachutist jumps from a n airplane, falls fr eely for 10 seconds and
then opens his parachute. Assume the parachutist's initial downward
velocity was v(O) = 0 ft/sec, assume the air resistance is proportional to
vl.^8 , and assume the constant of proportionality without the parachute