Question

A car of mass 1,435 kg traveling east and a truck of equal mass traveling north collide and become entangled, moving as a unit at 15.2 m/s and 64.5 degree north of east. Find the following. (a) the speed of the car prior to the collision m/s. (b) the speed of the truck prior to the collision.

Answer 1

To find the speed of the car prior to the collision, we can use the law of conservation of momentum. By substituting the given values into the equation, we can solve for the velocity of the car. Similarly, we can find the velocity of the truck prior to the collision using the same equation.

Step-by-step explanation:

To find the speed of the car prior to the collision, we need to use the law of conservation of momentum. The momentum before the collision is equal to the momentum after the collision. So, we can write:

(mass of car)(velocity of car) + (mass of truck)(velocity of truck) = (mass of car + mass of truck)(velocity of wreckage)

Substituting the given values:

(1435 kg)(velocity of car) + (1435 kg)(0 m/s) = (1435 kg + 1435 kg)(15.2 m/s)

Simplifying this equation, we can solve for the velocity of the car:

velocity of car = [(1435 kg + 1435 kg)(15.2 m/s) - (1435 kg)(0 m/s)] / 1435 kg

Similarly, we can find the velocity of the truck prior to the collision using the equation:

(mass of car)(velocity of car) + (mass of truck)(velocity of truck) = (mass of car + mass of truck)(velocity of wreckage)

Substituting the given values:

(1435 kg)(0 m/s) + (1435 kg)(velocity of truck) = (1435 kg + 1435 kg)(15.2 m/s)

Simplifying this equation, we can solve for the velocity of the truck:

velocity of truck = [(1435 kg + 1435 kg)(15.2 m/s) - (1435 kg)(0 m/s)] / 1435 kg