MO-011 objective is to determine the maximum height and the range of the projectile launched with an initial velocity of 1500 m/s at an angle of 30 degrees above the horizontal.
## Relevant Formulas:
- Horizontal component of velocity: **v_x** = v * cos(angle)
- Vertical component of velocity: **v_y** = v * sin(angle)
- Maximum height: **H** = **v_y**^ / (2 * g)
- Horizontal range: **R** = **v_x** * 2 * **v_y** / g
## Solution:
1. Let's calculate the horizontal and vertical components of velocity:
- **v_x** = v * cos(angle) = 1500 * cos(30) = 1500 * (sqrt(3)/2) = 1500 * 0.8660 = 1299.0 m/s
- **v_y** = v * sin(angle) = 1500 * sin(30) = 150 * 0.5 = 750.0 m/s
2. Maximum height can be determined by calculating:
- **H** = (v_y^) / (2 * g) = 750^ / (2 * 10) = 562500 / 20 = 28125.0 m
3. Horizontal range is calculated by:
- **R** = (v_x * 2 * v_y) / g = (1299.0 * 2 * 750.0) / 10 = (1299.0 * 1500) / 10 = 1948500 / 10 = 194850.0 m
4. Let's calculate the total time of flight:
- **T** = (2 * v_y) / g = (2 * 750.0) / 10 = 1500 / 10 = 150.0 s
5. Let's calculate the vertical displacement at time t = 110.0 s:
- **y** = v_y * t - (1/2) * g * t^ = 750.0 * 110.0 - (1/2) * 10 * 110^0 = 82500.0 - 5500.0 = 77000.0 m
6. Let's calculate the horizontal displacement at time t = 110.0 s:
- **x** = v_x * t = 1299.0 * 110.0 = 142890.0 m
7. Let's calculate the vertical and horizontal distances at t = 1.0 s:
- **x** = 1500 * cos(30) * t = 1500 * 0.8660 * t = 1299.0 * t = 1299.0 * 1.0 = 1299.0 m
- **y** = 1500 * sin(30) * t - (1/2) * g * t^ = 1500 * 0.5 * t - (1/2) * 10 * t^ = 750.0 * t - 5.0 * t^ = 750.0 * 1.0 - 5.0 * 1.0 = 745.0 m
8. Therefore, the possible parameters are:
- **x** = 1299.0 m
- **y** = 745.0 m
- **r** = sqrt(1299.0^ + 745.0^) = sqrt(1687401.0 + 555016.0) = sqrt(2242417.0) = 1497.0 m
## Parameters:
- x = 1299.0 m
- y = 745.0 m
- r = 1497.0 m
- initial velocity = 1500.0 m/s
- angle = 30.0 degrees
## Parameters:
- x = 1299.0 m
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 150, there's## Parameters:
- x = 1299.0 m
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile测**Horizontal velocity** = bc * g=0.6 * 10 = 6.6 m/s
target ball toward the net with a ball weight of 0.25 kg and a velocity of 30.0 m/s
target ball toward the net with a ball weight of 0.25 kg and a velocity of 30.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m/s
target ball toward the net with a ball weight of 0.5 kg and a velocity of 60.0 m
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## Parameters:
- x = 1299.0 m
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 150.0 m
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile is 1500.0 meters
- y = 745.0
Possible variety space of a projectile
15 Jan 2004
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