Part V: Calculations

Kinematic Formulas:

1. Calculate the height:

    a. Rocket I: 

• Acceleration: 4.9 m/s²
• Time: 3.8 seconds
• 1 meter = 3.28 feet 
• Y = Vi(t) + ½(a_v)(t²)
• Y = (0)(4.7) + ½(4.9)(3.8)²
• Y = 0 + 35.78
• Y = 35.37 ≈ 35.4 meters 
• Y = (35.4)(3.28) ≈ 116.1 feet
• Y = Vi(t) + ½(a_v)(t²)
• 116.1 = Vi(3.8) + ½(4.9)(3.8)²
• 3.8Vi = 97.18
• Vi = 11.9 ≈ 12 m/s

    b. Rocket II:

• Acceleration: 4.9 m/s²
• Time: 3.5 seconds
• 1 meter = 3.28 feet 
• Y = Vi(t) + ½(a_v)(t²)
• Y= (0)(3.5) + ½(4.9)(3.5)²
• Y = 0 + 30.0125 
• Y = 30.0125 ≈ 30 meters 
• Y = (30)(3.28) = 98.4 feet
• Y = Vi(t) + ½(a_v)(t²)
• 98.4 = Vi(3.5)  + ½(4.9)(3.5)²
• 3.5Vi = 38.37
• Vi = 10.96  ≈ 11 m/s
• For rocket I, the apex (highest point) was 115.8 feet. 
• For rocket II, the highest point was 98.4 feet.

2. Calculate the initial velocity:

    a. Rocket I: 

• Vi = 12 m/s

    b. Rocket II: 

• Vi = 11 m/s

3. Force body diagrams (free body diagrams):

    a. Rocket lifting off launch pad:

   b. Rocket at the highest point:

All Stages (ascent to descent):