Aroman 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

  the grams     of oxygen gas   that can be produced     is 20.6   grams of o₂

calculation

2liclo₃ →   2 licl + 3 o₂

step 1:   find the moles of liclo₃

moles = mass÷ molar mass

from periodic table the molar mass of liclo₃ =6.9 +35.5   +(16 x3) =90.4 g/mol

moles=38.7 g÷90.4 g/mol=0.4281   moles

step 2:   use the   mole ratio   to calculate the moles of o2

from equation above, liclo₃: o₂   is 2: 3  

therefore the moles of   o₂=0.4281 moles x3/2 =0.6422   moles

step 3: find mass   of o₂

mass= moles x molar mass

from periodic table the   molar mass of   o₂ = 16 x2= 32 g/mol

mass=0.6422   moles   x   32 g/mol = 20.6 grams of o₂

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s