v(t) = 300-32t
s(t) = 300t-16t^2
max s = 1406.25
(d) dv/dt = 300-32t-.0025v
v = 13100e^(-.0025t) - 12800
v=0 at x=9.267
s = 5240000(1-e^(-.0025t))-12800t
max s = 1384.7
Suppose a small cannonball weighing 16 pounds is shot vertically upward with an initial
velocity Vo = 300 ft/s
.
a) Construct the mathematical model.
b) Suppose air resistance is ignored, determine the velocity of the cannonball at any time t.
c) Using the result obtained in part (a), determine the height s(t) of the cannonball
measured from the ground level. Determine the maximum height attained by the
cannonball.
d) Assume that air resistance is proportional to instantaneous velocity v(t). Show that in this
case the maximum height attained by the cannonball is less than that in part (b), by
supposing that the constant of proportionality is k = 0.0025.
2 answers
How u got that V(t) = 300 - 32t
4 answers