Question

An object is traveling such that it has a momentum of magnitude 23.3 kg · m/s and a kinetic energy of 297 j. determine the following.

A.) _____ m/s
B.)_____ kg

Answer 1

Using the provided momentum and kinetic energy, the object's mass is calculated to be approximately 0.91 kg and its velocity is approximately 25.6 m/s.

Step-by-step explanation:

We have been given the momentum of an object as 23.3 kg · m/s and its kinetic energy as 297 J, and we need to find the object's velocity and mass. Recall the definitions of momentum (p = mv, where m is mass and v is velocity) and kinetic energy (KE = 0.5mv2).

First, we rewrite the kinetic energy equation in terms of momentum: KE = p2/(2m). Substituting the provided values, 297 J = (23.3 kg · m/s)2 / (2m), we can solve for mass m. After solving for m, we can use the momentum equation with our found mass to solve for velocity v.

Let's solve for the mass first:

1. 297 J = (23.32)/(2m)
2. 297 J * 2m = 23.32
3. m = 23.32 / (2 * 297 J)
4. m ≈ 0.91 kg

Now we calculate the velocity:

1. p = mv
2. 23.3 kg · m/s = 0.91 kg * v
3. v ≈ 25.6 m/s

The mass of the object is approximately 0.91 kg, and its velocity is approximately 25.6 m/s.

Answer 2

The object is traveling at approximately 10.33 m/s and has a mass of 2.25 kg.

Step-by-step explanation:

The magnitude of momentum of an object is given by the formula: p = mv

Given that the magnitude of the momentum is 23.3 kg · m/s, we can write the equation as: 23.3 kg · m/s = m × v

The kinetic energy of an object is given by the formula: KE = 0.5mv²

Given that the kinetic energy is 297 J, we can write the equation as 297 J = 0.5m × v²

To solve for v, we can use the first equation to express v in terms of p and m: v = p / m

Substituting this into the second equation, we get: 297 J = 0.5m × (p / m)²

Simplifying, we find: v = √((2 × 297 J) / m)

Plugging in the given values, we can calculate v to be approximately 10.33 m/s. To find the mass, we use the first equation: 23.3 kg · m/s = m × 10.33 m/s

Solving for m, we find: m = 2.25 kg

Therefore, the answers are:

A.) 10.33 m/s

B.) 2.25 kg