Effect of Lowered Center of Gravity on Jumping Time

[ravsterphysics]

Homework Statement

Homework Equations

The Attempt at a Solution

For part a) I got t=0.571 seconds
For part b) I got s=4.6m

But part c) is what I'm stuck on. If his centre of gravity has shifted lower by 50cm, is his time spent in the air greater?

 

[BvU]

Good assumption! so let him take off as a block of 2 m high and shrink to a block of 1 m high (with the same mass)

 

[haruspex]

But part c) is what I'm stuck on. If his centre of gravity has shifted lower by 50cm, is his time spent in the air greater

In solving parts a and b, you treated the athlete as a point particle. What point would it make sense to use?

 

[ravsterphysics]

Good assumption! so let him take off as a block of 2 m high and shrink to a block of 1 m high (with the same mass)

In solving parts a and b, you treated the athlete as a point particle. What point would it make sense to use?

i guess what I don't undestand is why his time spent in the air increases when he lands with lower center of gravity??

and working with that assumption, does that mean his max vertical distance has increased by 50cm?

 

[haruspex]

does that mean his max vertical distance has increased by 50cm?

Yes.

 

[ehild]

See the picture. He jumps with his foot reaching the ground. The red spot shows the centre of mass, it is about 1 m high above the ground.
During the jump, he lifts his legs, and he lands with his bottom reaching the ground. The final position of the centre of mass is 50 cm deeper than the initial height.