1) 80 kg vampire and 250kg werewolf clash during the Feat of Strength part of th
ID: 2260682 • Letter: 1
Question
1) 80 kg vampire and 250kg werewolf clash during the Feat of Strength part of the annual celebration of Festivus. The werewolf velocity just before the clash is 20m/s and is directed downwards, while the vampire velocity at the moment of the collision is 50m/s and is directed upwards. They clash in midair exactly 10 metres above the ground. Find how much time will they be airborne after the collision. /treat collision as inelastic/.
2) A 4.0-kg equilateral triangle, a 2.0-kg circle, a 6.0-kg square and a 1.0-kg rod form a system shown below. What is the centre of mass of this system? /L(rod)=D(circle)=W(triangle)=W(square)=3m/
80 kg vampire and 250kg werewolf clash during the Feat of Strength part of the annual celebration of Festivus. The werewolf velocity just before the clash is 20m/s and is directed downwards, while the vampire velocity at the moment of the collision is 50m/s and is directed upwards. They clash in midair exactly 10 meters above the ground. Find how much time will they be airborne after the collision. /treat collision as inelastic/. A 4.0-kg equilateral triangle, a 2.0-kg circle, a 6.0-kg square and a 1.0-kg rod form a system shown below. What is the centre of mass of this system? /L(rod)=D(circle)=W(triangle)=W(square)=3m/Explanation / Answer
1) m1 = 80 kg, m2 = 250 kg
v1 = 50 m/s, v2 = -20 m/s
let v is the velocity after the collison
m1*u1+m2*u2 = (m1+m2)*v
v = (m1*u1+m2*u2)/(m1+m2)
v = (80*50-250*20)/(80+250)
v = -3.03 m/s( down watd)
here g = 9.8 m/s^2
let t is the time taken
y = voy*t + 0.5*g*t^2
10 = 3.03*t + 4.9*t^2
4.9*t^2 +3.03*t - 10 = 0
solving this eqn we get, t = 1.252 s
2)
center of mass of trinagle
m1 = 4 kg
x1 = -1.5 m
y1 = +0.87 m
center of mass of circle
m2 = 2kg
x2 = -1.5 m
y2 = -3 m
center of mass of square
m3 = 6 kg
x3 = -1.5 m
y3 = -1.5 m
center of mass of rod
m4 = 1 kg
x4 = -1.5 m
y4 = +1.5 m
Xcm = (m1*x1+m2*x2+m3*x3+m4*x4)/(m1+m2+m3+m4)
Xcm = -1.5 cm
Ycm = (m1*y1+m2*y2+m3*y3+m4*y4)/(m1+m2+m3+m4)
Ycm = -0.704 m
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