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
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