What is the speed and direction of the third fragment?

Question

An isolated 3 kg object initially at rest explodes into 3 fragments. One fragment hass a mass of .50 kg and flies off along the negative x axis at a speed of 2.8 meters per second, and another has a mass of 1.3 kg and flies off along the negative y axis at a speed of 1.5 m/s. What is the speed and direction of the third fragment?

Answer 1

I thought so.

Momentum in x and y direction must be conserved.
since momentum originally is zero
0=p1+p2+p3 (this is a vector equation)
p1= - 0.50 x 2.8= -1.4 kg m/s (neg x-axis or 180 degrees)
p2= - 1.3 x 1.5= -1.95 kg m/s (neg y-axis or 270 degrees)

m3= 3.0- (0.5 +1.3)= 1.2kg

p3= Px3 + Py3 (vector eqiuation ) or
p3= Px3i + Py3j

Px3=-p1= 1.4 kg m/s (0 degrees)
Py3=-p2= 1.95 kg m/s (90 degrees)

Vx3= Px3/m3= 1.4/1.2= 1.17 m/s
Vy3= Py3/m3=1.95/1.2=1.63 m/s

Answer 2

this is a conservation of momentum problem ... since there are no external forces action on the object (it is isolated).

the inital momentum must equal the final momentum.

since momentum is a vector quantity, we set up two separate equations, one for momentum in the x direction and one for momentum in the y direction.

the initial state consists of a single particle at rest, therefore pix = piy = 0 (kg m/s)

the final state consists of three fragments so the x and y components of the momentum of the final system can be expressed as

pfx = p1fx + p2fx + p3fx
pfy = p1fy + p2fy + p3fy
since p=mv, px = mvx, py=vmy
for particle 1
m1 = 0.5kg
v1x = -2.8 m/s
v1y = 0 m/x
for particle 2
m2 = 1.3kg
v2x = 0 m/x
v2y = -1.5 m/s
for particle 3
m3 = 3.0kg - m1 - m2 = 1.2kg
solve for v3x and v3y from the conservation of momentum equations

Answer 3

enable North and East be beneficial guidelines through conservation of momentum: 0 = m1v1 + m2v2 + m3v3 Substituting: x: 0 = m(-2.8 + 0 + Vx) y: 0 = m(0 + -a million.4 + Vy) Vx = 2.8 m/s Vy = a million.4 m/s perspective: A = tan (Vy/Vx) A = arctan(a million.4/2.8) V^2 = Vx^2 + Vy^2 V = 3.13 m/s @ 26.565 * North of East