How Long to Accelerate a Projectile to Orbital Speed?

AI Thread Summary
Scientists are developing a gun designed to accelerate projectiles to orbital speeds, with a test achieving 4.29 km/s for a 5.0 kg projectile using a net force of 0.47 MN. To determine the time required for this acceleration, the formula F = ma is applied, resulting in an acceleration of 92,000 m/s². Using the change in velocity (Δv) and the calculated acceleration, the time (t) to reach the desired speed is found to be approximately 0.047 seconds. This highlights the feasibility of using such technology for launching payloads into orbit. The discussion emphasizes the importance of understanding impulse and acceleration in this context.
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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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