If a dog can jump 4ft high and a flea can jump 9ft high, how high can a flea jump off jumping dog?

Question

Mathematicians, please, answer here:

http://answers.yahoo.com/question/index?qid=20071218150616AAAHJtM&r=w

Answer 1

The initial velocity of the dog is sqrt(2*32*4)=16 ft/sec
The initial velocity of the flea (relative to the dog) is sqrt(2*32*9)=24 ft/sec.
Therefore, if the flea jumps immediately after the dog leaves the ground, it will have a velocity of 40 ft/sec relative to the ground. Maximum height will be 40^2/(32*2)=25 ft.

Answer 2

Hermoderus is correct IF AND ONLY IF the flea jumps in the same direction as the dog. If the flea jumps at an angle to the dog the result will be less. So the question should be re-phrased,
" What is the MAXIMUM HEIGHT a flea can jump off a jumping dog, if the dog can jump 4ft high and the flea can jump 9ft high?"

Answer 3

v fly relative to the dog v = sqr (2gh.flea)

v dog = sqr (2gh.dog)

v.fly = sqr (2gh.dog) + sqr(2gh.flea)

Height fly
h = 1/2* 1/g * (v.fly)^2
= 1/2 *1/g * [sqr (2gh.dog) + sqr(2gh.flea)]^2
= [sqr (h.dog) + sqr(h.flea)]^2
= [sqr (4) + sqr(9)]^2
= [2 + 3]^2
=25ft !!!!!!