That neighbor's pesky kid now has new missiles that make elastic collisions.

He insists on throwing 25.0 g rocks at your new 2.25 kg light fixture hanging by a 26.0 cm wire from the ceiling of your porch. If each rock strikes the fixture traveling at 10.0 m/s, how high will the light fixture go after it is hit by one of these new missiles?

h = ___ m

I got .057 m but it is incorrect.

You have to figure the velocity of the light fixture at collision time.

Use conservation of energy, and conservation of momentum.

Once you get the intial velocity of the light fixture,

1/2 masslight*velocitylight^2=masslight*g*height and solve for h

To solve this problem, we can use the principle of conservation of momentum and the principle of conservation of mechanical energy.

First, let's calculate the initial momentum of the rock and the light fixture before the collision. The momentum is given by the product of mass and velocity.

Initial momentum of the rock = (mass of the rock) x (velocity of the rock)
= 0.025 kg x 10.0 m/s
= 0.25 kg m/s

Initial momentum of the light fixture = (mass of the light fixture) x (velocity of the light fixture)
= 2.25 kg x 0 m/s (as the light fixture is initially at rest)
= 0 kg m/s

According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.

Total initial momentum = Total final momentum

0.25 kg m/s = (mass of the rock) x (final velocity of the rock) + (mass of the light fixture) x (final velocity of the light fixture)

Since the rock sticks to the light fixture after the collision, the final velocity of the rock and the final velocity of the light fixture will be the same.

Final velocity of the rock and the light fixture = v

0.25 kg m/s = (0.025 kg + 2.25 kg) x v
0.25 kg m/s = 2.275 kg x v

Now, let's calculate the height to which the light fixture will rise after the collision.

We can use the principle of conservation of mechanical energy. The initial mechanical energy is equal to the final mechanical energy.

Initial mechanical energy = Final mechanical energy

(Initial potential energy of the light fixture) + (Initial kinetic energy of the light fixture and the rock) = (Final potential energy of the light fixture) + (Final kinetic energy of the light fixture and the rock)

The initial potential energy of the light fixture is zero since it is at the starting position. The initial kinetic energy is given by:

Initial kinetic energy of the light fixture and the rock = (1/2) x (total mass) x (initial velocity)^2
= (1/2) x (2.275 kg) x (10.0 m/s)^2

The final potential energy is equal to:

Final potential energy of the light fixture = (mass of the light fixture) x (acceleration due to gravity) x (height)

We need to solve for the height of the light fixture, so we rearrange the equation:

(height) = (Final potential energy of the light fixture) / ((mass of the light fixture) x (acceleration due to gravity))

Substituting the values:

(height) = [(2.25 kg) x (9.8 m/s^2) x (25 g)] / [(2.275 kg) x (10.0 m/s)^2]

After evaluating this expression, the height should be approximately 0.00613 m or 6.13 mm.

Therefore, the height to which the light fixture will rise after being hit by one of these new missiles is approximately 0.00613 m.