How Long to Accelerate a Projectile to Orbital Speed?

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SUMMARY

The discussion focuses on calculating the time required to accelerate a 5.0 kg projectile to an orbital speed of 4.29 km/s using a net force of 0.47 MN. The acceleration is determined to be 92,000 m/s², leading to the conclusion that the time required for the projectile to reach this speed is 0.047 seconds. The calculations utilize Newton's second law (F = ma) and the kinematic equation Δv = a * t.

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  • Understanding of Newton's second law (F = ma)
  • Knowledge of kinematic equations, specifically Δv = a * t
  • Familiarity with units of force (Newtons) and mass (kilograms)
  • Basic grasp of impulse and its relevance in physics
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kiwisj
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Scientists are experimenting with a kind of gun that may eventually be used to fire payloads directly into orbit. In one test, this gun accelerates a 5.0 kg projectile from rest to a speed of 4.29 km s-1. The net force accelerating the projectile is 0.47 MN. How much time is required for the projectile to come up to speed? (Answer to 2 s.f.)

I have absolutely no idea how to do this...Any help is appreciated! Thanks
 
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Welcome to PF kiwisj.

Have you learned about impulse?
Can you give a definition or some relevant formula for it? Or describe in words what it is?
What units does it have?
 
Last edited:
F = ma
F= 0.47 MN= 4.7E5 N
m= 5 kg

Plug it in and solve for a ...

a=92000 m/s^2

Δv = a * t
Δv= 4.29km/s= 4290 m/s
a=92000 m/s^2

Solve for t and I got ...

t = 0.047s
 

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