The drawing shows two frictionless inclines that begin at ground level (h = 0 m) and slope upward at the same angle 0. One track is longer than the other, however. Identical blocks are projected up each track with the same initial speed vo. 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 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 vo = 7.00 m/s, and each incline slopes upward at an angle of 0 = 50.0°. The block on the shorter track leaves the track at a height of H₁ = 1.25 m above the ground. Show all of your work. LA H Longer track Shorter track

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Chapter1: Units, Trigonometry. And Vectors
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I know this website says only to submit one question at a time but this word problem has 12 questions to answer. If you can only answer one at a time I guess we can start with #3. all help is greatly appreciated, please see the attachment.

Thank you,

Miguel 

The drawing shows two frictionless inclines that begin at ground level (h = 0 m) and slope upward at the same angle θ. One track is longer than the other, however. Identical blocks are projected up each track with the same initial speed v₀. 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 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 = 7.00 m/s, and each incline slopes upward at an angle of θ = 50.0°. The block on the shorter track leaves the track at a height of H₁ = 1.25 m above the ground. Show all of your work.

*Diagram Description:*

- *Longer Track*: 
  - Shows an inclined plane with a block sliding upward, starting at ground level with initial speed v₀ and angle θ. The block reaches a height H.

- *Shorter Track*: 
  - Shows an inclined plane of shorter length with a block sliding upward and leaving the track at height H₁. The angle of inclination is θ. The block follows a projectile motion reaching an additional height H₂ above the end of the track.

**Questions and Steps for Analysis:**

1. List the known quantities in the scenario.
2. Convert all quantities to fundamental units.
3. Find the height H for the block on the longer track.
4. What is the potential energy of the block on the longer track for height H?
5. What is the kinetic energy of the block on the longer track for height H?
6. Find the total height H₁ + H₂ for the block on the shorter track.
7. What is the potential energy of the block on the shorter track for height H₁?
8. What is the kinetic energy of the block on the shorter track for height H₁?
9. What is the potential energy of the block on the shorter track for height H₂?
10. What is the kinetic energy of the block on the shorter track for height H₂?
11. What
Transcribed Image Text:The drawing shows two frictionless inclines that begin at ground level (h = 0 m) and slope upward at the same angle θ. One track is longer than the other, however. Identical blocks are projected up each track with the same initial speed v₀. 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 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 = 7.00 m/s, and each incline slopes upward at an angle of θ = 50.0°. The block on the shorter track leaves the track at a height of H₁ = 1.25 m above the ground. Show all of your work. *Diagram Description:* - *Longer Track*: - Shows an inclined plane with a block sliding upward, starting at ground level with initial speed v₀ and angle θ. The block reaches a height H. - *Shorter Track*: - Shows an inclined plane of shorter length with a block sliding upward and leaving the track at height H₁. The angle of inclination is θ. The block follows a projectile motion reaching an additional height H₂ above the end of the track. **Questions and Steps for Analysis:** 1. List the known quantities in the scenario. 2. Convert all quantities to fundamental units. 3. Find the height H for the block on the longer track. 4. What is the potential energy of the block on the longer track for height H? 5. What is the kinetic energy of the block on the longer track for height H? 6. Find the total height H₁ + H₂ for the block on the shorter track. 7. What is the potential energy of the block on the shorter track for height H₁? 8. What is the kinetic energy of the block on the shorter track for height H₁? 9. What is the potential energy of the block on the shorter track for height H₂? 10. What is the kinetic energy of the block on the shorter track for height H₂? 11. What
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