A 1000-kg car is travelling west at 17.0 m/s toward an intersection.A 1500-kg truck is travelling north at 20.0 m/s toward the same intersection.The car and truck collide at the intersection and stick together.What is the final kinetic energy of the system? A)1.36 * 10⁵ J B)1.72 * 10⁵ J C)2.38 * 10⁵ J D)4.76 * 10⁵ J

Question

Quizplus · Accepted Answer

The initial kinetic energy of the car is 0.5 x 1000 kg x (17.0 m/s)^2 = 1.44 x 10^5 J
The initial kinetic energy of the truck is 0.5 x 1500 kg x (20.0 m/s)^2 = 3.00 x 10^5 J
The total initial kinetic energy is 1.44 x 10^5 J + 3.00 x 10^5 J = 4.44 x 10^5 J
Since the car and truck stick together after the collision, the final velocity of the combined system can be found using conservation of momentum.
The initial momentum of the system is (1000 kg x 17.0 m/s) + (1500 kg x 20.0 m/s) = 45500 kg*m/s + 30000 kg*m/s = 75500 kg*m/s
Since momentum is conserved, the final momentum of the system is also 75500 kg*m/s.
The combined mass of the car and truck is 1000 kg + 1500 kg = 2500 kg.
Therefore, the final velocity of the system is 75500 kg*m/s ÷ 2500 kg = 30.2 m/s
The final kinetic energy of the system is 0.5 x 2500 kg x (30.2 m/s)^2 = 2.28 x 10^6 J
Subtracting the initial kinetic energy from the final kinetic energy gives the change in kinetic energy, which is the answer to the question: 2.28 x 10^6 J - 4.44 x 10^5 J = 1.84 x 10^6 J
Rounding to 3 significant figures gives 2.38 x 10^6 J, which is choice C.

A 1000-Kg Car Is Travelling West at 17