Collision: In reconstructing an automobile accident, investigators study the total momentum, both before and after the accident, of the vehicles involved. The total momentum of two vehicles moving in the same direction is found by multiplying the weight of each vehicle by its speed and then adding the results.19 For example, if one vehicle weighs 3000 pounds and is traveling at 35 miles per hour, and another weighs 2500 pounds and is traveling at 45 miles per hour in the same direction, then the total momentum is 3000 × 35 + 2500 × 45 = 217,500. In this exercise we study a collision in which a vehicle weighing 3000 pounds ran into the rear of a vehicle weighing 2000 pounds.
a. After the collision, the larger vehicle was traveling at 30 miles per hour, and the smaller vehicle was traveling at 45 miles per hour. Find the total momentum of the vehicles after the collision.
b. The smaller vehicle was traveling at 30 miles per hour before the collision, but the speed V , in miles per hour, of the larger vehicle before the collision is unknown. Find a formula expressing the total momentum of the vehicles before the collision as a function of V.
c. The principle of conservation of momentum states that the total momentum before the collision equals the total momentum after the collision. Using this principle with parts a and b, determine at what speed the larger vehicle was traveling before the collision.