A Roman centurion fires off a vat of burning pitch from

hiscatapult at 18.2m/s, 37 degrees above the horizontal.

a. how long was the vat in the air?

b. determine the horizontal component of the initial

velocityof the vat.

c. determine the range of the vat.

(a) 1.11sec

(b) 14.37m/s

(c) 31.78m

Explanation:

U = 18m/s, A = 37°, g = 9.8m/s^2

(a) t = UsinA/g = 18sin37°/9.8 = 18*0.6018/9.8 = 1.11sec

(b) Ux = UcosA = 18cos37° = 18*0.7986 = 14.37m/s

(c) R = U^2sin2A/g = 18^2sin2 (37°) / 9.8 = 324sin74°/9.8 = 324*0.9613/9.8 = 31.78m

a 5.995m

b 14.54m/s

C 31.84m

Explanation:

H = u^2 sin^2x/2g

H = 18.2^2 sin^2*37/2*10

H = 331.24 * 0.362/20

H = 5.995m

Horizontal component of the Vat

Ux = ucos x; x is the angle

Ux = 18.2 cos 37

Ux = 14.54m/s

Range = u^2 sin2x/g

18.2^2 sin 74/10

Range = 318.40/10

Range = 31.84m