Paintball Physics

By Michelle Lu

Kids often bruise when they are hit by a paintball if they’re not wearing a vest.
Let’s see how much force a paintball would be exerting on you if you were hit by a
paintball.

I chose to assume there is no air resistance. Target is at a distance of 50 ft and you
are shooting at an angle of 15° at 300 ft/s. The ball stops in 0.001s once it hits the
target.

m = 3.2 g = 0.0032 kg
vo = 300 ft/s = 91.4 m/s
v0x = 91.4cos15 = 88.3 m/s
voy = 91.4 sin15 = 23.67 m/s
Θ = 15°
Δx = 50 ft = 15.24 m

Δx = voxt + 1/2at2
15.24 = 88.3 t + 0
t = 0.17 s

Δy = vot + 1/2at2
Δy = (23.67 m/s)(0.17s) + ½(-9.8 m/s2) (0.17s)2
Δy = 3.88 m

vfy2 = voy2 + 2aΔy
vfy2 = (23.67 m/s)2 + 2(-9.8 m/s2)(3.88 m)
vfy = 22.0 m/s

vf = (vfx2 + vfy2)1/2
vf = (88.32 + 22.02)1/2
vf = 91 m/s

F = Δp/t
F =m(vf – vi)/t
F = [(0.0032 kg)(0 m/s – 91 m/s)]/0.001t
F = 291 N