Center of MassHard
Question
Two particles of equal mass m are projected form the ground with speed v1 and v2 at angle θ1 and θ2 as shown in figure. The centre of mass of the two particles
Options
A.will move in a parabolic path for any values of v1, v2, θ1 and θ2
B.can move in a vertical line
C.can move in a horizontal line
D.will move in a straight line for any value of v1, v2, θ1 and θ2
Solution
Centre of mass will move in a vertical line if v1 cos θ1 = v2 cos θ2. Otherwise for any other values it will follow a parabolic path.
Mathod II.
= V1 cosθ1 î + (V1 sinθ1 − gt) ĵ 
Parabolic path
= − V2 cosθ2 î + (V2 sinθ2 − gt) ĵ 
Parabolic path
= 
If
= 0 [Centre of mass of the Particle move only along Y axis ]
v1 cos θ1 − v2 cos θ2 = 0 ⇒ v1 cos θ1 = v2 cos θ2
then path may be straight line.
Mathod II.
= V1 cosθ1 î + (V1 sinθ1 − gt) ĵ Parabolic path = − V2 cosθ2 î + (V2 sinθ2 − gt) ĵ Parabolic path = If
= 0 [Centre of mass of the Particle move only along Y axis ]v1 cos θ1 − v2 cos θ2 = 0 ⇒ v1 cos θ1 = v2 cos θ2
then path may be straight line.
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