Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 62_H

In Fig. 8.38, a block slides along a path that is without friction until the block reaches the section of length \( L = 0.75 \text{ m} \), which begins at height \( h = 2.0 \text{ m} \) on a ramp of angle \( \theta = 30^\circ \). In that section, the coefficient of kinetic friction is \( 0.40 \). The block passes through point \( A \) with a speed of \( 8.0 \text{ m/s} \). If the block can reach point \( B \) (where the friction ends), what is its speed there, and if it cannot, what is its greatest height above \( A \)?