MathDB

A projectile moves in a resisting medium. The resisting force is a function of the velocity and is directed along the velocity vector. The equation

x=f(t)

(where

f(t)

is not constant) gives the horizontal distance in terms of the time

t

. Show that the vertical distance

y

is given by

y=-gf(t) \int \frac{dt}{f'(t)} + g \int \frac{f(t)}{f'(t)} \, dt +Af(t)+B

where

A

and

B

are constants and

g

is the acceleration due to gravity.

B6