h(x) = ² + vot + ho 2 And the expression that calculates the horizontal distance (in meters) a projectile travels when fired out of a railgun at a 45 degree angle is; 9 Where: h(t) is the height function of the projectile in meters • Vo is the starting velocity of the projectile (m/s) • ho is the starting height of the projectile • g is the gravitational constant (m/s²) for your selected planetary body • t, your independent variable, is time in seconds While developing our railgun, we build it with a barrel length of 100 meters firing out at a 45 degree angle, giving us a starting height of 70.7 meters at the tip of the barrel. Our rail gun can accelerate a projectile up to a speed of 16,000 meters per second. How far would your test projectile travel before it hits the ground (in km), and how long would this take (in minutes)? And is our railgun sufficient to break the escape velocity of your selected planetary body?
h(x) = ² + vot + ho 2 And the expression that calculates the horizontal distance (in meters) a projectile travels when fired out of a railgun at a 45 degree angle is; 9 Where: h(t) is the height function of the projectile in meters • Vo is the starting velocity of the projectile (m/s) • ho is the starting height of the projectile • g is the gravitational constant (m/s²) for your selected planetary body • t, your independent variable, is time in seconds While developing our railgun, we build it with a barrel length of 100 meters firing out at a 45 degree angle, giving us a starting height of 70.7 meters at the tip of the barrel. Our rail gun can accelerate a projectile up to a speed of 16,000 meters per second. How far would your test projectile travel before it hits the ground (in km), and how long would this take (in minutes)? And is our railgun sufficient to break the escape velocity of your selected planetary body?
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Diameter 139,820 km
· Density 1326 kg/m3
· Gravity 24.79 m/s2
· Mass (1024kg) : 1898
· Escape Velocity (km/s):59.5
The H max= 71.40x10^6m
T= 2400 sec or 40 min
giving these info please help me solve the issue in the pic
![### Projectile Motion: Understanding Railgun Physics
#### Equation for Height Function
The height function of a projectile fired from a railgun is given by the equation:
\[ h(t) = -\frac{g}{2}t^2 + v_0 t + h_0 \]
#### Equation for Horizontal Distance
The expression that calculates the horizontal distance (in meters) a projectile travels when fired out of a railgun at a 45-degree angle is:
\[ \frac{v_0^2}{g} \]
#### Explanation of Variables:
- **\( h(t) \)**: Height function of the projectile in meters.
- **\( v_0 \)**: Starting velocity of the projectile (m/s).
- **\( h_0 \)**: Starting height of the projectile.
- **\( g \)**: Gravitational constant (m/s²) for your selected planetary body.
- **\( t \)**: Independent variable representing time in seconds.
### Example Scenario
While developing our railgun, we build it with a barrel length of 100 meters firing out at a 45-degree angle. This setup gives us a starting height of 70.7 meters at the tip of the barrel. Our railgun can accelerate a projectile up to a speed of 16,000 meters per second.
To explore the effectiveness of this railgun:
1. **How far will the test projectile travel before it hits the ground (in km)?**
2. **How long will this take (in minutes)?**
3. **Is the railgun sufficient to break the escape velocity of your selected planetary body?**
#### Interpretation of the Example
Using the parameters:
- **Starting Height (\( h_0 \))**: 70.7 meters.
- **Initial Velocity (\( v_0 \))**: 16,000 meters per second.
We need to calculate the horizontal distance traveled and the time taken before the projectile hits the ground, and determine if this setup can achieve escape velocity for a given planet.
By solving these equations, one can learn about the practical applications and limitations of railgun technology in different gravitational fields.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F901908b8-e4a6-4b0b-9c6b-b07df73a0074%2Faa3fde65-6a0b-4cb7-8657-75eb027ed107%2Fpaymuch_processed.png&w=3840&q=75)
Transcribed Image Text:### Projectile Motion: Understanding Railgun Physics
#### Equation for Height Function
The height function of a projectile fired from a railgun is given by the equation:
\[ h(t) = -\frac{g}{2}t^2 + v_0 t + h_0 \]
#### Equation for Horizontal Distance
The expression that calculates the horizontal distance (in meters) a projectile travels when fired out of a railgun at a 45-degree angle is:
\[ \frac{v_0^2}{g} \]
#### Explanation of Variables:
- **\( h(t) \)**: Height function of the projectile in meters.
- **\( v_0 \)**: Starting velocity of the projectile (m/s).
- **\( h_0 \)**: Starting height of the projectile.
- **\( g \)**: Gravitational constant (m/s²) for your selected planetary body.
- **\( t \)**: Independent variable representing time in seconds.
### Example Scenario
While developing our railgun, we build it with a barrel length of 100 meters firing out at a 45-degree angle. This setup gives us a starting height of 70.7 meters at the tip of the barrel. Our railgun can accelerate a projectile up to a speed of 16,000 meters per second.
To explore the effectiveness of this railgun:
1. **How far will the test projectile travel before it hits the ground (in km)?**
2. **How long will this take (in minutes)?**
3. **Is the railgun sufficient to break the escape velocity of your selected planetary body?**
#### Interpretation of the Example
Using the parameters:
- **Starting Height (\( h_0 \))**: 70.7 meters.
- **Initial Velocity (\( v_0 \))**: 16,000 meters per second.
We need to calculate the horizontal distance traveled and the time taken before the projectile hits the ground, and determine if this setup can achieve escape velocity for a given planet.
By solving these equations, one can learn about the practical applications and limitations of railgun technology in different gravitational fields.
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