# Projectile Motion with air resistance

• PalashD

## Homework Statement

Consider a ball which is projected horizontally with speed u from the edge of a cliff of height H as shown in the Fig. (1). There is air resistance proportional to the velocity in both x and y direction i.e. the motion in the x (y) direction has air resistance given by the $c v_x (c v_y)$ where c is the proportionality constant and $v_x(v_y)$ is the velocity in the x (y) directions. Take the downward direction to be negative. The acceleration due to
gravity is g. Take the origin of the system to be at the bottom of the cliff as shown in Fig. (1).
(a) Obtain expression for x(t) and y(t).
(b) Obtain the expression for the equation of trajectory.
(c) Make a qualitative, comparative sketch of the trajectories with and without air resistance.
(d) Given that height of cliff is 500 m and c = 0.05 sec^−1. Obtain the approximate time
in which the ball reaches the ground. Take g = 10 m-sec^−2

Figure 1:http://img24.imageshack.us/img24/8558/aaaaqvy.th.jpg [Broken]T

## The Attempt at a Solution

I just want to know that here do we have to take $c v_x(c v_y)$ as a force or something else?

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They want you to evaluate the effect of drag in the linear regime where the force is related to velocity by the coefficient c. So the product of c*v is the force. Contained within c are the the influences from the viscosity of the air and the cross section that the object presents to the air.

Okay! Thanks