Question

Two cars, both of mass (m), collide and stick together. Prior to the collision, one car was traveling North at speed (2v), while the second was traveling East at speed v. Neglecting horizontal obstacles, what is the resulting velocity of the cars after the collision?

Answer 1

The resulting velocity after the collision of the two cars, that were initially moving North at speed 2v and East at speed v respectively, is sqrt{5} * v and the direction is 26.57 degrees East from North.

Step-by-step explanation:

This problem entails the analysis of an inelastic collision, specifically where two objects stick together after collision. The principle of conservation of momentum is pivotal here. The total momentum of the two cars before the collision must equal the total momentum after the collision, since no external force is acting on the system.

Mathematically, the momentum conservation is presented by the formula M1 V1 + M2 V2 = (M1 + M2) V', where v' is the shared final velocity for both objects since they are stuck together. In this particular example, both cars have equal masses (m), thus simplifying the equation significantly. The first car's initial velocity is 2v (in the North direction) and the second's is v (East). After the collision, the two cars move together at a velocity whose magnitude and direction can be obtained using vector addition.

The resulting velocity, v', is a vector sum of the velocities of the individual cars before the collision. This can be easily computed using the Pythagorean theorem. Hence, the magnitude of the resulting velocity is sqrt{(2v)^2 + v^2}, which equals sqrt{5} * v. The direction of this velocity from the North can be computed as tan^-1(v / 2v), which equals 26.57 degrees East of North.

Learn more about Inelastic Collision