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two particles are launched from the origin of the coordinate system at time t =

ID: 1396330 • Letter: T

Question

two particles are launched from the origin of the coordinate system at time t

= 0. Particle 1 of mass m1 = 5.60 g is shot directly along the x axis (on a frictionless floor), where it moves with a constant speed of 12.3 m/s. Particle 2 of mass m2 = 2.10 g is shot with a velocity of magnitude 16.3 m/s, at an upward angle such that it always stays directly above particle 1 during its flight. (a) What is the maximum height Hmax reached by the com of the two-particle system? In unit-vector notation, what are the (b) velocity and (c) acceleration of the com when the com reaches Hmax?

Explanation / Answer

a)
let

m1 = 5.6 grams, m2 = 2.1 grams

vo1 = 12.3 m/s

vo2 = 16.3 m/s and theta is the angle of projection.

from the given data, vo2x = vo1

vo2*cos(theta) = vo1

theta = cos^-1(vo1/vo2)

= cos^-1(12.3/16.3)

= 41 degrees.

s0, maximum height reached by m2, H = vo2^2*sin^2(41)/(2*g)

= 16.3^2*sin^2(41)/(2*9.8)

= 5.83 m


Ycm = (m1*y1 + m2*y2)/(m1+m2)

= (5.6*0 +2.1*5.83)/(5.6+2.1)

= 1.59 m <<<<<<<<---------------------Answer

b) Vcm = (m1*vo1 + m2*vo2x)/(m1+m2)

= (5.6*12.3 + 2.1*12.3)/(5.6 + 2.1)

= 12.3 m/s <<<<<<<<---------------------Answer

c) acm = g

= 9.8 m/s^2 <<<<<<<<---------------------Answer