Laws of Motion · Question 2

A projectile of mass 200 g is launched in a viscous medium at an angle 60 with the horizontal, with an initial velocity of 270 m/s. It experiences a viscous drag force F=-c v where the drag coefficient c=0.1 kg/s and v is the instantaneous velocity of the projectile. The projectile hits a vertical wall after 2 s. Taking e=2.7, the horizontal distance of the wall from the point of projection (in m) is

Answer

167 to 171

Solution

Horizontal: m dvxdt=-cvx vx=uxe-ct/m, with cm=0.5 s-1

x= muxc (1-e-ct/m ), ux=270 60 =135 m/s

x= 0.2 1350.1 (1-e-1 )=270 (1- 12.7 )=270 1.72.7=170 m

Answer: 170