Question

Topic - center of mass and linear momentum:
A 15 kg package is moving at a speed of 10.0m/s vertically upward along a y-axis when it explodes intro three fragments: a 2.00kg fragment is shot upward with an initial speed of 20.0m/s and a 3.00 kg fragment is shot in the positive direction of a horizontal x axis with an initial speed of 5.00m/s.

Find a) the speed of the third fragment right after the explosion.
b) the total kinetic energ provided by the explosion.

Answer 1

a)
Let

M = 15 kg, V = 10 m/s

m1 = 2 kg, v1 = 20 m/s (towards +y)

m2 = 3 kg, v2 = 5 m/s (towards +x)

m3 = 15 - (2+3)

= 10 kg

Let v3 is the veloicty of m3.

Apply conservation momentum in x-direction.

M*vx = m1*v1x + m2*v2x + m3*v3x

0 = 0 + 3*5 + 10*v3x

==> v3x = -15/10

= -1.5 m/s

Apply conservation momentum in y-direction.

M*vy = m1*v1y + m2*v2y + m3*v3y

15*10 = 2*20 + 0 + 10*v3y

==> v3y = (150 - 40)/10

= 11 m/s

so, v3 = sqrt(v3x^2 + v3y^2)

= sqrt(1.5^2 + 11^2)

= 11.1 m/s <<<<<<<<<<<<<<<<<-------------Answer

b) Total kinetic energy provided by the explosion = KEf - KEi

= (0.5*m1*v1^2 + 0.5*m2*v2^2 + 0.5*m3*v3^2) - 0.5*M*V^2

= 0.5*2*20^2 + 0.5*3*5^2 + 0.5*10*11.1^2 - 0.5*15*10^2

= 303.55 J <<<<<<<<<<<<<<<<<-------------Answer