Maximum Jump Height of a 12-kg Dog: A Physics Problem

[Luhertz]

Homework Statement

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?

Homework Equations

Change in gravitational potential energy = mgΔx
Work = Force * Force Displacement

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.

 

[haruspex]

how high can he jump?

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.

 

[Luhertz]

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.

1.15 m worked! Thanks for the assurance.