# Bee and a spiral

1. Jan 20, 2009

### chaotixmonjuish

1.)

A bee goes from its hive in a spiral path given in plane polar coordinates by
r = b*ekt , θ = ct,
where b, k, c are positive constants. Show that the angle between the velocity vector and the
acceleration vector remains constant as the bee moves outward. (Hint: Find v · a/va.)

so here is my v and a

2.)
v = (r')er+(r*θ')eθ

a = (r''+rθ')er+(rθ''+2r'θ')eθ

r' = bk*ekt
r'' = bk2ekt
θ' = c

3.) my attempt at a solution

bkekt(bk2ekt-bektc2)+(bektc)(2bkektc)

is that the right dot product

this is where i'm stuck

2. Jan 20, 2009

### chaotixmonjuish

so I got down to this:

e2kt(a bunch of constants)+e2kt(a bunch of constants)/e4kt

all the e's cancelled out and left just constants

3. Dec 7, 2011

### markpace123

My answer is for the dot product is:

e2kt(b2k3 + b2kc + 2b2kc2)

4. Dec 7, 2011

### markpace123

you continue by finding the modulus of v and a then by using the hint you cross out the

b2e2kt and end up with cos-1(a bunch of constants) and the answer