# Newton's third law -- Calculate the recoil of a paintball gun

Homework Statement:
A paintball with a mass of 0.15 kg is fired from a paintball gun that has a mass of 5.5 kg. The paintball leaves the gun with a velocity of 45 m/s [N] having accelerated for 0.10 s. Calculate the acceleration of the paintball gun.
Relevant Equations:
Givens:
Mass of paintball = 0.15 kg
Mass of paintball gun = 5.5 kg
initial velocity of paintball = 45 m/s [N]
time = 0.10 s
I've been stuck on this for sometime now, and am unsure how to approach this question.

nrqed
Homework Helper
Gold Member
Homework Statement:: A paintball with a mass of 0.15 kg is fired from a paintball gun that has a mass of 5.5 kg. The paintball leaves the gun with a velocity of 45 m/s [N] having accelerated for 0.10 s. Calculate the acceleration of the paintball gun.
Relevant Equations:: Givens:
Mass of paintball = 0.15 kg
Mass of paintball gun = 5.5 kg
initial velocity of paintball = 45 m/s [N]
time = 0.10 s

I've been stuck on this for sometime now, and am unsure how to approach this question.
First find the force on the paintball (hint: use Newton's second law).

First find the force on the paintball (hint: use Newton's second law).
I'm confused, in order to find the net force you would need acceleration, wouldn't you?

nrqed
Homework Helper
Gold Member
I'm confused, in order to find the net force you would need acceleration, wouldn't you?
Yes, and you can calculate the acceleration. You know the speed of ejection and the time it took to accelerate the paintball.

Yes, and you can calculate the acceleration. You know the speed of ejection and the time it took to accelerate the paintball.
I think I got it:

a= vf-vi/t
a= 0 m/s- 45 m/s [N] / 0.10 s
a= -450 m/s^2 [N]
a= 450m/s

(this is the paintball)
Fnet= ma
Fnet= (0.15 kg) x(450 m/s^2 )
Fnet= 68 N

(this is the paintball gun)
Fnet= ma
a= Fnet/m
a= 68 N / 5.5 kg
a= 12 m/s^2

can you check if I did this right please?
(Sorry about the black lines I don't know how to fix that)

nrqed
• 