A 5-kg projectile is fired from a cannon barrel of length 2m, the explosive force exerted on the projectile, while it is in the barrel, varies in the manner shown. Determine the approximate muzle velocity of the projectile at the instant it leaves the barrel. Neglect the frictional effects inside the barrel, the barrel is horizontal.

1) 2.75 km/s
2) 3.34 km/s
3) 4.58 km/s
4) 5.32 km/s

The work done is measured as the area under the force - displacement curve. This area is approximately 28 squares. Since the area under each curve is
A = 5 (106) (0.2) = 106

T1 + S U1-2 = T2
1/2 (5) (v12) + [(28) A] = 1/2 (5) (v22)
0 + [(2) 106] = 1/2 (7) (v22), since v12 = 0
v2 = 3346.64 m/s = 3.34 km/s

So the exit velocity of the projectile is
v2 = 3.34 km/s