In the figure, two particles are launched from the origin of the coordinate syst

Question

In the figure, two particles are launched from the origin of the coordinate system at time t = 0. Particle 1 of mass m1 = 6.80 g is shot directly along the x axis (on a frictionless floor), where it moves with a constant speed of 10.8 m/s. Particle 2 of mass m2 = 3.40 g is shot with a velocity of magnitude 25.0 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)

both moves with same horizontal velocity

s0, 10.8 = 25 cos(theta)

theta = 64.4 deg

max height is reached when vertical component of 2 will become zero.

vy = 0

v0y = 25 sin64.4 = 22.55 m/s

vy^2 - v0y^2 = 2 a d

0^2 - 22.55^2 = 2(-9.8 ) (Hmax)

Hmax= 25.94 m

for centre of mass,

Hmax = [ (25.94 x 3.40) + (6.80 x 0 )] / (3.40 + 6.80)

= 8.65 m

(B) Vcm = 10.8 i

(C) a = [ (-9.8j x 3.40) ] / (3.40 + 6.80)

a = - 3.27 j m/s^2

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