# Touch and go

**Classical Mechanics**Level 4

A cylinder of mass 4kg and radius 5m has a fixed axis passing through its center of mass and is at some height from the ground. A particle of mass 1kg is projected from the ground with initial velocity 50m/s making an angle 53° with the horizontal such that it grazes the top of the cylinder when at maximum height. Find the horizontal displacement of the particle before striking the ground.

g = \( 10m/{ s }^{ 2 } \)

\( \sin { 53° } =\frac { 4 }{ 5 } \)

\( \cos { 53° } =\frac { 3 }{ 5 } \)

Assume friction is sufficiently high so that slipping ceases before the two bodies lose contact.

This problem is originally part of set Mechanics problems by Abhishek Sharma.

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