Question

A 13-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 0.30 m .

Part A 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? Express your answer with the appropriate units. hmax hmax = .86m

Answer 1

Gravitational force=mg=130N (taking g as 10)
Maximum force exerted by dog = 2.1 * 130=273N
Acceleration on dog due to normal force=273/13= 21 m/s2
Velocity acquired when the dog reaches 0.3m from 0.1m:
V2 =2 * (21-10) * 0.5 which gives us V=3.31 m/s

Maximum height obtained from this position= v2 /2g =0.55m

Hence max height above ground=0.55m + 0.3m =0.85m

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