An object has a kinetic energy of 329 J and a momentum of magnitude 22.3 kg·m/s.

To solve this problem, we need to understand the relationships between kinetic energy and momentum, as well as how to calculate each of them.

1. Kinetic Energy (KE):
Kinetic energy is the energy possessed by an object due to its motion. It can be calculated using the formula:

KE = (1/2) * m * v^2

where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.

2. Momentum (p):
Momentum is the product of an object's mass and its velocity. It can be calculated using the formula:

p = m * v

where p is the momentum, m is the mass of the object, and v is the velocity of the object.

Now, let's use the given information to solve the problem.

Given:
Kinetic energy (KE) = 329 J
Momentum (p) = 22.3 kg·m/s

We'll solve for the mass (m) and velocity (v).

First, let's find the mass (m) using the momentum formula:

p = m * v

22.3 kg·m/s = m * v

Since we don't have the velocity (v), we can't directly solve for the mass.

However, we know that momentum is the product of mass (m) and velocity (v), and we have the value for momentum (22.3 kg·m/s). So, there must be an infinite number of combinations of mass and velocity that can yield that momentum.

Now, let's find the velocity (v) using the kinetic energy formula:

KE = (1/2) * m * v^2

329 J = (1/2) * m * v^2

We don't have the mass (m) and velocity (v) separately, so we can't directly solve for either of them from this equation.

In conclusion, given only the kinetic energy and momentum of an object, we cannot determine the mass and velocity of the object individually. We need additional information to solve the problem.