Chapter 6, Problem 48P

The drawing shows two frictionless inclines that begin at ground level $\left(h=\text{om}\right)$ and slope upward at the same angle $\theta .$ One track is longer than the other, however. Identical blocks are projected up each track with the same initial speed $v_0.$ On the longer track the block slides upward until it reaches a maximum height $H$ above the ground. On the shorter track the block slides upward, flies off the end of the track at a height $H_1$ above the ground, and then follows the familiar parabolic trajectory of projectile motion. At the highest point of this trajectory, the block is a height ${\text{H}}_2$ above the end of the track. The initial total mechanical energy of each block is the same and is all kinetic energy. The initial speed of each block is $v_0=7.00 \text{m}/\text{s},$ and each incline slopes upward at an angle of $\theta =50.0°.$ The block on the shorter track leaves the track at a height of $H_1=1.25 \text{m}$ above the ground. Find

1. the height $H$ for the block on the longer track and
2. the total height ${\text{H}}_1+{\text{H}}_2$ for the block on the shorter track.