How fast must an 816-kg Volkswagen travel to have the same momentum as a 2,650-kg Cadillac going 10 mph?

To determine the speed at which the 816-kg Volkswagen must travel to have the same momentum as the 2,650-kg Cadillac going 10 mph, we need to use the formula for momentum: Momentum (p) = mass (m) × velocity (v) Let's calculate the momentum of the Cadillac first: Mass of the Cadillac (m1) = 2,650 kg Velocity of the Cadillac (v1) = 10 mph Convert the velocity of the Cadillac from mph to m/s: 1 mph = 0.44704 m/s Velocity of the Cadillac (v1) = 10 mph × 0.44704 m/s = 4.4704 m/s Momentum of the Cadillac (p1) = m1 × v1 Momentum of the Cadillac (p1) = 2,650 kg × 4.4704 m/s ≈ 11,826.96 kg·m/s Now, let's find the velocity at which the Volkswagen must travel to have the same momentum: Mass of the Volkswagen (m2) = 816 kg Velocity of the Volkswagen (v2) = ? We can set up the equation using the principle of conservation of momentum: Momentum of the Cadillac (p1) = Momentum of the Volkswagen (p2) m1 × v1 = m2 × v2 Substituting the known values: 2,650 kg × 4.4704 m/s = 816 kg × v2 11,826.96 kg·m/s = 816 kg × v2 Divide both sides by 816 kg: v2 = 11,826.96 kg·m/s / 816 kg v2 ≈ 14.49 m/s Therefore, the Volkswagen must travel at approximately 14.49 m/s (or 51.97 km/h) to have the same momentum as the Cadillac going 10 mph.