The incline is frictionless, this means we can use the conservation of energy: the initial kinetic energy of the block
[tex]K= \frac{1}{2}mv^2 [/tex]
is converted into gravitational potential energy
[tex]U=mgh[/tex]
where h is the height reached by the block as it stops. By equalizing the two formulas, we get
[tex] \frac{1}{2} mv^2=mgh[/tex]
[tex]h= \frac{v^2}{2g}= \frac{(12.0 m/s)^2}{2(9.81 m/s^2)} =7.3 m [/tex]
However, this is the maximum height reached by the block. The distance along the surface of the plane is given by:
[tex]d= \frac{h}{\sin 20^{\circ}}= \frac{7.3 m}{\sin 20^{\circ}}=21.3 m [/tex]
