Consider two cars, one a compact model (m = 781 kg) and the other an SUV (m = 2483 kg). The SUV is traveling at 15 m/s, while the compact car is traveling at an unknown speed v. If the two cars have the same momentum, what is v?

m1V1 - m2V2,

781V1 = 2483 * 15 = 37,245,
V1 = 47.7 m/s.

To solve this problem, we can use the principle of conservation of momentum. The momentum of an object is defined as the product of its mass and velocity.

Let's denote the momentum of the compact car as p_compact and the momentum of the SUV as p_SUV.

The momentum of an object can be calculated using the equation:
p = m * v

Given:
Mass of compact car (m_compact) = 781 kg
Mass of SUV (m_SUV) = 2483 kg
Velocity of SUV (v_SUV) = 15 m/s

The momentum of the SUV (p_SUV) can be calculated using its mass and velocity:
p_SUV = m_SUV * v_SUV
= 2483 kg * 15 m/s

Since the two cars have the same momentum, we can set p_compact equal to p_SUV:
p_compact = p_SUV

Now, we can plug in the known values and solve for the unknown velocity of the compact car (v_compact):

m_compact * v_compact = m_SUV * v_SUV

781 kg * v_compact = 2483 kg * 15 m/s

To solve for v_compact, we can rearrange the equation and solve for v_compact:

v_compact = (m_SUV * v_SUV) / m_compact

Substituting the given values:

v_compact = (2483 kg * 15 m/s) / 781 kg

Now, we can calculate the value using a calculator:

v_compact ≈ 47.42 m/s

Therefore, the unknown speed v of the compact car is approximately 47.42 m/s.