A Bates motor is a solid rocket motor with grains cast into multiple separate segments. each a cylindrical shape as shown. (Actually the sides taper in slightly. so the cross section is really trapezoidal instead of rectangular, but we will ignore this aspect here.) (21} Find an expression for the burning surface area A of one motor segment, in terms of r1. r; and to. Note that both ends burn as well as the inner bore of the cylinder. (b) As a motor segment burns the burning surface recedes at a rate I". Find an expression for the rate A at which the burning surface area changes. in terms of r'. (c) For a neutral burn (constant thrust). the burning surface area mUst be. constant. What is the relation among r... r; and w such that A is zero? ((1) Another desirable characteristic of a Bates motor is that the segments should burn to the wall at the same time as. or before. the width it? goes to zero. What is the relation among r1. r; and it: such that the burn is neutral and r. becomes equal to r; ti.e.. the segment burns to the wall) at the same time as it! goes to zero