Find (a) the height H for the block on the longer track and (b) the total height

Question

Find (a) the height H for the block on the longer track and (b) the total height H1 + H2 for the block on the shorter track.

a) H= 2.401 m

b) H1 + H2 = _______ m

*HELP WITH PART B PLEASEEE*

The drawing shows two frictionless inclines that begin at ground level (h = 0 m) 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 v0. One 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 H1 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 H2 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 v0 = 6.86 m/s, and each incline slopes upward at an angle of Theta = 52.5 Degree . The block on the shorter track leaves the track at a height of H1 = 1.13 m above the ground. Find (a) the height H for the block on the longer track and (b) the total height H1 + H2 for the block on the shorter track. a) H= 2.401 m b) H1 + H2 = _______ m *HELP WITH PART B PLEASEEE*

Explanation / Answer

let v1 be the speed at H1 the energy conservation law between the heigth H1 and heighest point H1 + H2 gives    ( 1/2) m( v1c os)2 + mg ( H1 + H2) = ( 1/2) mv12 + mg H1            H1 + H2 = v12 ( 1- cos2 ) + 2g H1/2g applying law of conservation between intial position and H1 ( 1/2) mv12 + mgH1 = ( 1/2) mv02      v1 = v02 - 2gH1          =( 6.86 m/s)2 - 2 ( 9.8 m/s2)1.13 m          = 4.99 m/s H1 + H2 = ( 4.99 m/s)2 ( 1- cos2 52.50) +2 ( 9.8 m/s2)( 1.13 m)/ 2( 9.8 m/s2)                = 1.92 m          =( 6.86 m/s)2 - 2 ( 9.8 m/s2)1.13 m          = 4.99 m/s H1 + H2 = ( 4.99 m/s)2 ( 1- cos2 52.50) +2 ( 9.8 m/s2)( 1.13 m)/ 2( 9.8 m/s2)                = 1.92 m

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