Projectile Launch - Using Earth's Radius

In summary, the launch speed of a projectile that rises vertically above the Earth to an altitude equal to 14 Rearth before coming to rest momentarily is 10802 m/s. The total mechanical energy at launch and at maximum altitude are related by the equation sqrt{2GM(\\frac{1}{R_e}-\\frac{1}{14R_e})}.
  • #1
bustin
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1. What is the launch speed of a projectile that rises vertically above the Earth to an altitude equal to 14 Rearth before coming to rest momentarily?

Homework Equations

sqrt{2GM(\\frac{1}{R_e}-\\frac{1}{14R_e})}

The Attempt at a Solution



G= 6.67x10^11
M=5.97x10^24
R_e=6.37x10^6

I get 2988 m/s I know its wrong but I gave it a shot. This is for online homework. Any help would be very nice. Thanks in advance
 
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  • #2
What is the total mechanical energy at launch? At maximum altitude? How do these relate?
 
  • #3
i tried to look into that but I couldn't find much info in my book. could you be more specific?
 
  • #4
i finally got it. i got 10802 m/s.

thanks for the tip
 

Related to Projectile Launch - Using Earth's Radius

1. How does Earth's radius affect projectile launch?

Earth's radius plays a crucial role in projectile launch as it determines the maximum distance a projectile can travel before hitting the ground. This is because the radius of Earth affects the curvature of its surface, which in turn affects the trajectory of the projectile.

2. Can a projectile be launched from any point on Earth's surface?

Yes, a projectile can be launched from any point on Earth's surface as long as the launch velocity and angle are within the limits of the Earth's gravitational pull. However, the distance and trajectory of the projectile may vary depending on the launch point due to the varying curvature of Earth's surface.

3. How does the launch angle affect the distance traveled?

The launch angle has a significant impact on the distance traveled by a projectile. The optimal launch angle for achieving maximum distance is 45 degrees, as it allows the projectile to travel the furthest due to the combination of horizontal and vertical velocities.

4. Is the Earth's rotation considered in projectile launch calculations?

Yes, the Earth's rotation is taken into account in projectile launch calculations. The Coriolis effect, which is the apparent deflection of moving objects on a rotating planet, must be considered when calculating the trajectory of a projectile launched from Earth's surface.

5. How does air resistance affect projectile launch using Earth's radius?

Air resistance can significantly impact the distance and trajectory of a projectile launched using Earth's radius. The denser the air, the greater the resistance, which can cause the projectile to lose speed and height, resulting in a shorter distance traveled. This is why projectiles launched in vacuum conditions can travel much farther than those launched in a dense atmosphere.

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