One particle, mass m1, is fired vertically upwards with an initial velocity v0 f

Question

One particle, mass m1, is fired vertically upwards with an initial velocity v0 from the
ground (height y = 0). At the same time (t = 0), another particle, mass m2, is released
from rest at a height y = h, directly above the first, where h > 0. The particles are then
in free fall near the earth's surface. Air resistance and the rotation of the earth may be
neglected.
a) Write equations for the vertical positions y1 and y2 of the particles as
functions of time t from their launch, before any collision.
b) Write an equation for the position ycm of the centre of mass of the two
particles as a function of time. Simplify your expression by removing any
common factors.

Explanation / Answer

s = ut -.5gt^2 y1 = v0t -.5gt^2 y2 = h - (0 +.5gt^2) center of mass is at m1y1+m2y2/(m1+m2) substitute to find the correct value Also note that the equation of y1 and y2 are valid only for the time before the collision with the ground.

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