Can Machine Gun Bullets Propel a Vehicle to Required Speeds?

[bcjochim07]

Homework Statement

The Army of the Nation of Whynot has a plan to propel small vehicles across the battlefield by shooting them, from behind, with a machine gun. They've hired you as a consultant to help with an upcoming test. A 100 kg test vehicle will roll along frictionless rails. The vehicle has a tall "sail" made of ultrahard steel. Previous tests have shown that a 20.0g bullet traveling at 400 m/s rebounds from the sail at 100 m/s. The design objective is for the cart to reach a speed of 19.0 m/s in 30.0 s . You need to tell them how many bullets to fire per second from the machine gun. Note that your answer should be a rate, which can be fractional, rather than a quantity, which must be an integer.

Homework Equations

p=mv J=change in momentum

The Attempt at a Solution

I found the impulse exerted on a bullet.
J=(.02kg)(-100m/s)-(.02kg)(400m/s)
J= -10 Ns

Then I set up an equation to find what impulse needs to be exerted on the cart to speed up to 19 m/s:

0kgm/s + J = (100kg)(19 m/s)
J=1900 Ns

Then I assumed the impulse exerted on a bullet is the same as the impulse exerted on the sail by a single bullet :

1900Ns* (1 bullet/10Ns) =190 bullets
I then divided that by 30 sec. & came up with 6.33 bullets/sec.

Is this correct?

 

[Kaleb]

Your math is correct and I ran through your procedure and it looks sound.

 

[tiny-tim]

… Because … Because … Because … !

The Nation of Because regards your militaristic experiments as a threat to our beliefs!

The ancient Nation of Because will always defeat the Nation of Whynot!

Go to your room! ​