Rocket sled A rocket sled moves along a horizontal plane, and is retarded by a friction force f friction = μ W , where μ is constant and W is the weight of the sled. The sled’s initial mass is M , and...

1. 
   

   
   
   Rocket
   
   
   
   
   sled
   
   

   
   

A rocket sled moves along a horizontal plane, and is retarded by a friction force

f


_friction


=


μ


W

, where

μ

is constant and

W

is the weight of the sled.

The sled’s initial mass is

M

, and its rocket engine expels mass at constant rate

dM


/


dt

≡

γ

; the expelled mass has constant speed

v


₀

relative to the rocket.

The rocket sled starts from rest and the engine stops when half

the sled’s total mass is gone. Find an expression for the maximum speed.