A 64 kg skater, at rest on frictionless ice, tosses a 12 kg snowball with velocity by v = 53i+ 14.0j m/s, where the x- and y- axes are in the horizontal plane. Find x-component v(x) of the subsequent velocity of the skater. As well as Find y-component v(y) of the subsequent velocity of the skater.

To find the x-component (v(x)) of the subsequent velocity of the skater, we can use the law of conservation of momentum. According to this law, the initial momentum of the system (skater and snowball) will be equal to the final momentum of the system.

The initial momentum of the system is given by the formula:
P(initial) = (mass of skater) * (initial velocity of skater) + (mass of snowball) * (initial velocity of snowball)

Since the skater is initially at rest, the initial velocity of the skater is 0.

The final momentum of the system is given by the formula:
P(final) = (mass of skater) * (final velocity of skater) + (mass of snowball) * (final velocity of snowball)

We need to find the final velocity of the skater in the x-direction.

Using the conservation of momentum, we have:
P(initial) = P(final)

Substituting the given values:

(64 kg) * (0) + (12 kg) * (53 m/s) = (64 kg) * (v(x)) + (12 kg) * (v(x))

Simplifying the equation, we get:
(12 kg) * (53 m/s) = (76 kg) * (v(x))

Now, we can solve for v(x):
v(x) = (12 kg * 53 m/s) / 76 kg

Calculating the value:
v(x) ≈ 8.289 m/s

Therefore, the x-component (v(x)) of the subsequent velocity of the skater is approximately 8.289 m/s.

To find the y-component (v(y)) of the subsequent velocity of the skater, we can use the fact that there is no external force acting in the vertical direction (y-direction) since it is a frictionless surface.

Hence, the y-component of the velocity remains constant, which means v(y) = 14.0 m/s.

Therefore, the y-component (v(y)) of the subsequent velocity of the skater is 14.0 m/s.

a 12 kg snowball?? That is quite a snowball! Do you mean 12 g?

momentum before = 0 = momentum after
in x direction and in y direction.