A 15-kg dog jumps up in the air to catch a ball. The dog\'s center of mass is no

Question

A 15-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 0.50m .

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?

******* The answer is not 0.97m, 3.57m, 1.17m, 1.08m, or 0.72m

Explanation / Answer

push force = F = 2.1mg

s0,
F - mg = ma

a = 2.1mg -mg /m = 1.1mg/ m = 10.78 m/s2

veloicty gained pushing his Centre of mass form 0.10m to 0.50m

v^2 = 2 x 10.78 x (0.50 - 0.10)

v = 2.94 m/s

after that he left ground contact gravity will start to work

v^2 - u^2 = 2ad

0 - 2.94^2 = 2x - 9.8 x d

d = 0.44 m

total height form ground .

H = 0.44 + 0.50 = 0.94 m

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