# Maxinum Height Question

1. Nov 15, 2014

### Luhertz

1. The problem statement, all variables and given/known data
A 12-kg dog jumps up in the air to catch a ball. The dog's center of mass is normally 0.20 m above the ground, and he is 0.50 m long. The lowest he can get his center of mass is 0.10 m above the ground, and the highest he can get it before he can no longer push against the ground is 0.60m.

If the maximum force the dog can exert on the ground in pushing off is 2.1 times the gravitational force Earth exerts on him, how high can he jump?

2. Relevant equations
Change in gravitational potential energy = mgΔx
Work = Force * Force Displacement
3. The attempt at a solution
Dog pushes itself to 0.6 m, then from that point the change in position is given by:
0.5*(2.1mg - mg) = mgΔx
0.55 m = Δx

Δx + 0.6 m = 1.15 m

I'm not sure if 1.15 m is correct, but I do know that 1.05 m, 0.85 m, 1.5 m, and 0.74 m are incorrect.

2. Nov 15, 2014

### haruspex

Unfortunately, that's a bit vague. Does it mean
1. how high can it get its centre of mass?
2. how high can it reach?
3. how high a bar can it clear?
Assuming it means (1), I agree with your answer. If it means (2) you can add something based on the given info, or if it means (3) subtract a different number.

3. Nov 15, 2014

### Luhertz

1.15 m worked! Thanks for the assurance.