A 2.87 kg object initially moving in the positive x-direction with a velocity of +4.87 m/s collides with and sticks to a 1.96 kg object initially moving in the negative y-direction with a velocity of -2.55 m/s. Find the final components of velocity of the composite object. (Indicate the direction with the sign of your answer.)

Vfx=
Vfy=

Well, let's see what happens when these two objects decide to have a little collision party!

First, let's find the x-component of velocity for the composite object. Since the first object is initially moving in the positive x-direction and sticks to the second object, we can say that the x-component of velocity for the composite object should remain the same.

So, Vfx = +4.87 m/s.

Now, for the y-component of velocity. The second object is initially moving in the negative y-direction and sticks to the first object. This means that the final y-component of velocity should be the sum of the initial velocities of the two objects.

So, Vfy = (-2.55 m/s) + 0 m/s (because the first object only moves in the x-direction).

Therefore,

Vfx = +4.87 m/s (in the positive x-direction)
Vfy = -2.55 m/s (in the negative y-direction).

To find the final components of velocity of the composite object, we can apply the principles of conservation of momentum in both the x and y directions.

1. Conservation of momentum in the x-direction:

The initial momentum in the x-direction is given by:
m1 * v1x + m2 * v2x

Where m1 is the mass of the first object (2.87 kg), v1x is the velocity of the first object in the x-direction (+4.87 m/s), m2 is the mass of the second object (1.96 kg), and v2x is the velocity of the second object in the x-direction (0 m/s since it was initially moving in the negative y-direction).

The final momentum in the x-direction is given by:
(m1 + m2) * Vfx

Applying conservation of momentum:
m1 * v1x + m2 * v2x = (m1 + m2) * Vfx

Plugging in the given values:
(2.87 kg) * (+4.87 m/s) + (1.96 kg) * 0 m/s = (2.87 kg + 1.96 kg) * Vfx

Simplifying:
13.9949 kg*m/s = 4.83 kg * Vfx

Dividing both sides by 4.83 kg:
Vfx = 13.9949 kg*m/s / 4.83 kg
Vfx ≈ 2.895 m/s

The final component of velocity in the x-direction, Vfx, is approximately +2.895 m/s (positive because it is in the positive x-direction).

2. Conservation of momentum in the y-direction:

The initial momentum in the y-direction is given by:
m1 * v1y + m2 * v2y

Where v1y is the velocity of the first object in the y-direction (0 m/s since it was initially moving in the positive x-direction), and v2y is the velocity of the second object in the y-direction (-2.55 m/s).

The final momentum in the y-direction is given by:
(m1 + m2) * Vfy

Applying conservation of momentum:
m1 * v1y + m2 * v2y = (m1 + m2) * Vfy

Plugging in the given values:
(2.87 kg) * 0 m/s + (1.96 kg) * (-2.55 m/s) = (2.87 kg + 1.96 kg) * Vfy

Simplifying:
-5.008 kg*m/s = 4.83 kg * Vfy

Dividing both sides by 4.83 kg:
Vfy = -5.008 kg*m/s / 4.83 kg
Vfy ≈ -1.036 m/s

The final component of velocity in the y-direction, Vfy, is approximately -1.036 m/s (negative because it is in the negative y-direction).

Therefore, the final components of velocity of the composite object are:
Vfx ≈ 2.895 m/s (in the positive x-direction)
Vfy ≈ -1.036 m/s (in the negative y-direction)

To solve this problem, we can use the principles of conservation of momentum and conservation of kinetic energy.

1. Conservation of Momentum:
The total momentum before the collision is equal to the total momentum after the collision.
Initial momentum = Final momentum

The initial momentum is the sum of the momenta of the two objects:
m1 * v1_initial + m2 * v2_initial = (m1 + m2) * vf

m1 = mass of object 1 = 2.87 kg
v1_initial = initial velocity of object 1 in the x-direction = +4.87 m/s
m2 = mass of object 2 = 1.96 kg
v2_initial = initial velocity of object 2 in the y-direction = -2.55 m/s
vf = final velocity of the composite object

Plugging in the given values, we have:
(2.87 kg)(+4.87 m/s) + (1.96 kg)(-2.55 m/s) = (2.87 kg + 1.96 kg) * vf

2. Conservation of Kinetic Energy:
The total kinetic energy before the collision is equal to the total kinetic energy after the collision. Since the objects stick together after the collision, we consider the final kinetic energy of the composite object.

The initial kinetic energy is the sum of the kinetic energies of the two objects:
KE_initial = (1/2) * m1 * v1_initial^2 + (1/2) * m2 * v2_initial^2

The final kinetic energy is the kinetic energy of the composite object:
KE_final = (1/2) * (m1 + m2) * vf^2

Since the collision is perfectly inelastic, the kinetic energy is not conserved. However, we can use this equation to solve for vf.

Plugging in the given values, we have:
(1/2) * (2.87 kg) * (4.87 m/s)^2 + (1/2) * (1.96 kg) * (-2.55 m/s)^2 = (1/2) * (2.87 kg + 1.96 kg) * vf^2

Now, solve these two equations simultaneously to find vf.
Once you have vf, you can find the final components of velocity by decomposing it into x and y components. The sign of each component indicates the direction.
Vfx = vf * cos(θ)
Vfy = vf * sin(θ), where θ is the angle with respect to the x-axis.

conservation of momentum

intial momentum=final momentum
2.87*4.87i +1.96*(-2.55)j=(2.87+1.96)V

13.97i - 5j=4.83 V

solve for V. I used i,j instead of x,y