A ball of mass $m$ is rolling on the floor without sliding towards a vertical wall. Friction coefficient between the ball and the wall is $u$ and standard gravity is $g$. Ball and the wall are perfectly elastic with an infinite elasticity coefficient and the collision is very short.
What is the minimal velocity of the ball necessary for the ball to "jump" as a result of the collision?
My way of thinking:
Because the collision lasts is "very short" the force acting perpendicular to the surface of the wall on the ball is very large. Thus so is the friction. Thus the inertia is transformed into vertical motion. This would mean no matter the speed the ball would move up. This doesn't seem to be a correct answer though.
How to correctly calculate the velocity necessary given only the data in the text? Why is my approach incorrect?