Question

You want to close an open door by throwing either a 400-g lump of clay or a 400-g rubber ball toward it. you can throw either object with the same speed, but they are different in that the rubber ball bounces off the door while the clay just sticks to the door. which projectile will apply the larger impulse to the door and be more likely to close it and why?

Answer 1

Refer to the diagram shown below.

Let m =  the mass (g) of the door.
Let v =  the launch velocity
Let u =  the velocity of the door after impact.

Elastic impact (rubber ball):
The rubber ball bounces off the door with presumably elastic impact, which means that both momentum and kinetic energy are conserved.
Conservation of momentum requires that
400v = -400v + mu
Therefore
$u=( \frac{800}{m} )v$

Inelastic impact (clay):
The clay sticks to the door after impact.
Conservation of momentum requires that
400g = (m+400)u
Therefore
$u=( \frac{400}{m+400} )v$

When we compare magnitudes of u for the door, we find that
$u_{1}=( \frac{400}{m} )(2v), \,\, elastic \\\\ u_{2}=( \frac{400}{m+400} )v , \,\, inelastic$
Clearly, the elastic impact creates a greater value of u for the door.

Answer:
The rubber ball creates a larger impulse to the door because the nature of its impact is approximately elastic.